<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><Version>2.4.0.8</Version><ReportLongName>0018 - Disclosure - CREDIT FACILITY WITH PLATINUM-MONTAUR LIFE SCIENCES, LLC</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><CurrencyCode /><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName /><CurrencySymbol /><contextRef><ContextID>From2013-01-01to2013-06-30</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0001031927</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2013-01-01T00:00:00</PeriodStartDate><PeriodEndDate>2013-06-30T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS /><CurrencyCode /><OriginalCurrencyCode /></MCU><CurrencySymbol /><Labels><Label Key="CalendarSupplement" Id="0" Label="6 Months Ended" /><Label Key="Calendar" Id="1" Label="Jun. 30, 2013" /></Labels></Column></Columns><Rows><Row FlagID="0"><Id>1</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>1</Level><ElementName>ecte_NotesToFinancialStatementsAbstract</ElementName><ElementPrefix>ecte_</ElementPrefix><IsBaseElement>false</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:stringItemType</ElementDataType><SimpleDataType>string</SimpleDataType><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Notes to Financial Statements</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>ecte_CreditFacilityPlatinumMontaurLifeSciencesTextBlock</ElementName><ElementPrefix>ecte_</ElementPrefix><IsBaseElement>false</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="From2013-01-01to2013-06-30" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0; text-align: justify; text-indent: 9pt"&gt;&amp;#160;On August 31,
2012, the Company and Montaur entered into a Loan Agreement (the &amp;#147;Loan Agreement&amp;#148;) pursuant to which Montaur made a
non-revolving draw credit facility (the &amp;#147;Credit Facility&amp;#148;) of up to $20,000,000 available to the Company, a substantial
portion of which is subject to the successful achievement of certain clinical and regulatory milestones set forth in the Loan Agreement,
with an initial available principal amount of $5,000,000 (the &amp;#147;Maximum Draw Amount&amp;#148;).&amp;#160;&amp;#160;The Company issued
to Montaur a Promissory Note dated August 31, 2012 (the &amp;#147;Note&amp;#148;), with a maturity date of five years from the date of
closing (the &amp;#147;Maturity Date&amp;#148;).&amp;#160;&amp;#160;The Company has used the proceeds from the Credit Facility to fund operations.&lt;/p&gt;

&lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0; text-indent: 0.5in"&gt;&amp;#160;&lt;/p&gt;

&lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0; text-align: justify; text-indent: 9pt"&gt;&amp;#160;The principal
balance of each draw will bear interest from the applicable draw date at a rate of 10% per annum, compounded monthly.&amp;#160;&amp;#160;The
Company is required to make interest payments on the principal amount due in connection with each draw on the first business day
of each month until the Maturity Date.&amp;#160;&amp;#160;The Company is also required to make a mandatory prepayment on each interest
payment date of an amount equal to one-third of its total revenue for the then prior fiscal quarter, up to the maximum amount
outstanding under the Note at that time.&amp;#160;&amp;#160;The Company is not, however, required to make such interest payment or mandatory
prepayment if doing so would reduce the Company&amp;#146;s cash and cash equivalents to less than $5,000,000.&amp;#160;&amp;#160;Any amounts
not previously paid in full will be due and payable on the Maturity Date.&amp;#160;&amp;#160;The Company has the right to permanently
prepay any draw, in whole or in part, prior to the Maturity Date.&lt;/p&gt;

&lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0; text-align: justify; text-indent: 9pt"&gt;&amp;#160;&lt;/p&gt;

&lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0; text-align: justify; text-indent: 9pt"&gt;The Company&amp;#146;s subsidiary, Sontra Medical, Inc. (&amp;#147;Sontra&amp;#148;),
agreed to guarantee the obligations of the Company under the Note pursuant to a guaranty agreement entered into on August 31,
2012 (the &amp;#147;Guaranty&amp;#148;).&amp;#160;&amp;#160;Additionally, the Note is secured by the Pledged Revenue (as defined in the Loan
Agreement) of the Company and the Company&amp;#146;s subsidiaries pursuant to a Security Agreement dated as of August 31, 2012 by
and among the Company, Sontra and Montaur.&amp;#160;&amp;#160;Upon the earlier of the Maturity Date of the Note or an event of default,
as defined in the Loan Agreement, the Note shall be secured by substantially all of the assets of the Company and any of its subsidiaries,
which security interest shall not be effective until such event of default or maturity, pursuant to a Default Security Agreement
dated August 31, 2012 by and among the Company, Sontra and Montaur.&amp;#160;&amp;#160;The Company also has agreed to pay all costs associated
with registering the shares underlying the Warrants (should it choose to register such shares) and to indemnify Montaur from liability
resulting from the registration of such shares (subject to certain standard exceptions) in accordance with a Registration Indemnity
Agreement between the Company and Montaur.&lt;/p&gt;

&lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0; text-indent: 0.5in"&gt;&amp;#160;&lt;/p&gt;

&lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0; text-align: justify; text-indent: 9pt"&gt;&amp;#160;Pursuant to
the Loan Agreement, the Company issued Montaur a warrant to purchase 400,000 shares of its Common Stock, with a term of five years
and an exercise price of $20.00 per share (the &amp;#147;Commitment Warrant&amp;#148;).&amp;#160;&amp;#160;The fair value of the warrant was
determined to be approximately $4,840,000 and was recorded as a deferred financing cost that will be amortized to interest expense
over the term of the Note.&amp;#160;&amp;#160;Of this cost, $968,004 is reflected in Current Assets, representing the portion which will
be amortized over the next twelve months. Amortization of the deferred financing cost for the three and six months ended June 30,
2013 was $242,000 and $484,000, respectively, and is included in interest expense.&amp;#160;&amp;#160;In addition, for each $1,000,000
of funds borrowed pursuant to the Credit Facility, the Company will issue Montaur a warrant to purchase 100,000 shares of Common
Stock, with a term of five years and an exercise price equal to 150% of the market price of the Common Stock at the time of the
draw, but in no event less than $20.00 or more than $40.00 per share (together with the Commitment Warrant, the &amp;#147;Warrants&amp;#148;).&amp;#160;&amp;#160;All
of the Warrants are immediately exercisable and will have a term of five years from the issue date. The exercise price of the Warrants
is subject to adjustment for stock splits, combinations or similar events.&amp;#160;&amp;#160;An exercise under the Warrants may not result
in the holder beneficially owning more than 4.99% or 9.99%, as applicable, of all of the Common Stock outstanding at the time;
provided, however, that a holder may waive the 4.99% ownership limitation upon sixty-one (61)&amp;#160;days&amp;#146; advance written
notice to the Company.&lt;/p&gt;

&lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0; text-indent: 0.5in"&gt;&amp;#160;&lt;/p&gt;

&lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0; text-align: justify; text-indent: 9pt"&gt;&amp;#160;On September
14, 2012, the Company submitted a draw request to Montaur in the amount of $3,000,000 in the form required by the Loan Agreement
(the &amp;#147;September Request&amp;#148;).&amp;#160;&amp;#160;The Company ultimately received the $3,000,000 in the following increments: $1,000,000
on September 20, 2012, $500,000 on October 17, 2012, and $1,500,000 on November 6, 2012.&amp;#160;&amp;#160;These draws were recorded on
the Consolidated Balance Sheet under note payable, net of the initial $3,000,000 in discounts recorded related to the warrants
issued.&amp;#160;&amp;#160;In accordance with the Loan Agreement and as a result of funding received from Montaur, the Company issued to
Montaur separate warrants concurrent with the three draws above to purchase 100,000, 50,000 and 150,000 shares of Common Stock
each with a term of five years, and exercise prices of $21.30, $22.70 and $21.10 per share, respectively.&amp;#160;&amp;#160;The fair value
of the warrants issued to purchase 300,000 shares of Common Stock was determined to be approximately $3,455,000, of which $3,000,000
was treated as a debt discount and was to be accreted to interest expense over the term of the Note, and the balance of approximately
$455,000 was charged to interest expense in 2012.&lt;/p&gt;

&lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0; text-indent: 0.5in"&gt;&amp;#160;&lt;/p&gt;

&lt;p style="font: 10pt/normal Times New Roman, Times, Serif; margin: 0; text-align: justify; text-indent: 9pt"&gt;&amp;#160;On March 1,
2013, the Company elected to prepay all outstanding draws under the Montaur Credit Facility totaling $3,113,366, which includes
interest accrued and unpaid to that date of $113,366.&amp;#160;&amp;#160;After such date, no principal amount is outstanding under the
Credit Facility.&amp;#160;&amp;#160;Concurrent with this prepayment, the Company recorded non-cash interest expense of approximately $2,879,166
in March 2013 relating to the unamortized debt discount on the outstanding draws paid off.&lt;/p&gt;</NonNumbericText><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>nonnum:textBlockItemType</ElementDataType><SimpleDataType>na</SimpleDataType><ElementDefenition>CreditFacilityPlatinumMontaurLifeSciencesTextBlock</ElementDefenition><ElementReferences>No definition available.</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>NOTE 13. CREDIT FACILITY WITH PLATINUM-MONTAUR LIFE SCIENCES, LLC</Label></Row></Rows><Footnotes /><IsEquityReport>false</IsEquityReport><ReportName>CREDIT FACILITY WITH PLATINUM-MONTAUR LIFE SCIENCES, LLC</ReportName><MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel><SharesRoundingLevel>UnKnown</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>true</HasCustomUnits><IsEmbedReport>false</IsEmbedReport><IsMultiCurrency>false</IsMultiCurrency><ReportType>Sheet</ReportType><RoleURI>http://echotx.com/role/CreditFacilityWithPlatinum-MontaurLifeSciencesLlc</RoleURI><NumberOfCols>1</NumberOfCols><NumberOfRows>2</NumberOfRows></InstanceReport>
