﻿<?xml version="1.0" encoding="utf-8"?>
<InstanceReport xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema">
  <Version>2.2.0.7</Version>
  <hasSegments>false</hasSegments>
  <ReportName>Credit Facility</ReportName>
  <ReportLongName>0211 - Disclosure - Credit Facility</ReportLongName>
  <DisplayLabelColumn>true</DisplayLabelColumn>
  <ShowElementNames>false</ShowElementNames>
  <RoundingOption />
  <HasEmbeddedReports>false</HasEmbeddedReports>
  <Columns>
    <Column>
      <LabelColumn>false</LabelColumn>
      <Id>1</Id>
      <Labels>
        <Label Id="1" Label="6 Months Ended" />
        <Label Id="2" Label="Jun. 30, 2010" />
      </Labels>
      <CurrencyCode>USD</CurrencyCode>
      <FootnoteIndexer />
      <hasSegments>false</hasSegments>
      <hasScenarios>false</hasScenarios>
      <Segments />
      <Scenarios />
      <Units>
        <Unit>
          <UnitID>USD</UnitID>
          <UnitType>Standard</UnitType>
          <StandardMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema>
            <MeasureValue>USD</MeasureValue>
            <MeasureNamespace>iso4217</MeasureNamespace>
          </StandardMeasure>
          <Scale>0</Scale>
        </Unit>
        <Unit>
          <UnitID>USDEPS</UnitID>
          <UnitType>Divide</UnitType>
          <NumeratorMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema>
            <MeasureValue>USD</MeasureValue>
            <MeasureNamespace>iso4217</MeasureNamespace>
          </NumeratorMeasure>
          <DenominatorMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema>
            <MeasureValue>shares</MeasureValue>
            <MeasureNamespace>xbrli</MeasureNamespace>
          </DenominatorMeasure>
          <Scale>0</Scale>
        </Unit>
        <Unit>
          <UnitID>Shares</UnitID>
          <UnitType>Standard</UnitType>
          <StandardMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema>
            <MeasureValue>shares</MeasureValue>
            <MeasureNamespace>xbrli</MeasureNamespace>
          </StandardMeasure>
          <Scale>0</Scale>
        </Unit>
      </Units>
      <CurrencySymbol>$</CurrencySymbol>
    </Column>
  </Columns>
  <Rows>
    <Row>
      <Id>2</Id>
      <Label>Credit Facility [Abstract]</Label>
      <Level>0</Level>
      <ElementName>navg_CreditFacilityAbstract</ElementName>
      <ElementPrefix>navg</ElementPrefix>
      <IsBaseElement>false</IsBaseElement>
      <BalanceType>na</BalanceType>
      <PeriodType>duration</PeriodType>
      <ShortDefinition>Credit Facility Abstract.</ShortDefinition>
      <IsReportTitle>false</IsReportTitle>
      <IsSegmentTitle>false</IsSegmentTitle>
      <IsSubReportEnd>false</IsSubReportEnd>
      <IsCalendarTitle>false</IsCalendarTitle>
      <IsTuple>false</IsTuple>
      <IsAbstractGroupTitle>true</IsAbstractGroupTitle>
      <IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow>
      <IsEquityAdjustmentRow>false</IsEquityAdjustmentRow>
      <IsBeginningBalance>false</IsBeginningBalance>
      <IsEndingBalance>false</IsEndingBalance>
      <IsReverseSign>false</IsReverseSign>
      <PreferredLabelRole />
      <IsEPS>false</IsEPS>
      <FootnoteIndexer />
      <Cells>
        <Cell>
          <Id>1</Id>
          <ShowCurrencySymbol>false</ShowCurrencySymbol>
          <IsNumeric>false</IsNumeric>
          <IsRatio>false</IsRatio>
          <DisplayZeroAsNone>false</DisplayZeroAsNone>
          <NumericAmount>0</NumericAmount>
          <RoundedNumericAmount>0</RoundedNumericAmount>
          <NonNumbericText />
          <NonNumericTextHeader />
          <FootnoteIndexer />
          <hasSegments>false</hasSegments>
          <hasScenarios>false</hasScenarios>
          <DisplayDateInUSFormat>false</DisplayDateInUSFormat>
        </Cell>
      </Cells>
      <OriginalInstanceReportColumns />
      <ElementDataType>xbrli:stringItemType</ElementDataType>
      <SimpleDataType>string</SimpleDataType>
      <ElementDefenition>Credit Facility Abstract.</ElementDefenition>
      <IsTotalLabel>false</IsTotalLabel>
    </Row>
    <Row>
      <Id>3</Id>
      <Label>Credit Facility</Label>
      <Level>1</Level>
      <ElementName>navg_CreditFacilityTextBlock</ElementName>
      <ElementPrefix>navg</ElementPrefix>
      <IsBaseElement>false</IsBaseElement>
      <BalanceType>na</BalanceType>
      <PeriodType>duration</PeriodType>
      <ShortDefinition>Credit Facility Text Block.</ShortDefinition>
      <IsReportTitle>false</IsReportTitle>
      <IsSegmentTitle>false</IsSegmentTitle>
      <IsSubReportEnd>false</IsSubReportEnd>
      <IsCalendarTitle>false</IsCalendarTitle>
      <IsTuple>false</IsTuple>
      <IsAbstractGroupTitle>false</IsAbstractGroupTitle>
      <IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow>
      <IsEquityAdjustmentRow>false</IsEquityAdjustmentRow>
      <IsBeginningBalance>false</IsBeginningBalance>
      <IsEndingBalance>false</IsEndingBalance>
      <IsReverseSign>false</IsReverseSign>
      <PreferredLabelRole>verboselabel</PreferredLabelRole>
      <IsEPS>false</IsEPS>
      <FootnoteIndexer />
      <Cells>
        <Cell>
          <Id>1</Id>
          <ShowCurrencySymbol>false</ShowCurrencySymbol>
          <IsNumeric>false</IsNumeric>
          <IsRatio>false</IsRatio>
          <DisplayZeroAsNone>false</DisplayZeroAsNone>
          <NumericAmount>0</NumericAmount>
          <RoundedNumericAmount>0</RoundedNumericAmount>
          <NonNumbericText>&lt;!--DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd" --&gt;
   &lt;!-- Begin Block Tagged Note 11 - navg:CreditFacilityTextBlock--&gt;
   &lt;div style="font-family: 'Times New Roman',Times,serif; margin-left: 0in; "&gt;
   &lt;div align="justify" style="font-size: 10pt; margin-top: 10pt"&gt;&lt;b&gt;Note 11. Credit Facility&lt;/b&gt;
   &lt;/div&gt;
   &lt;div align="justify" style="font-size: 10pt; margin-top: 10pt"&gt;On April&amp;#160;1, 2010, we entered into a $140&amp;#160;million credit facility agreement entitled &amp;#8220;Fifth Amended
   and Restated Credit Agreement&amp;#8221; with JPMorgan Chase Bank, N.A., as Administrative Agent, and a
   syndicate of lenders. The credit facility is a letter of credit facility and amends and replaces
   the $75&amp;#160;million credit facility that expired by its terms on April&amp;#160;2, 2010. We may request that the
   facility be increased by an amount not to exceed $25&amp;#160;million. The credit facility, which is
   denominated in U.S. dollars, is utilized primarily by Navigators Corporate Underwriters Ltd. and
   Millennium Underwriting Ltd. to fund our participation in Syndicate 1221 through letters of credit.
   The letters of credit issued under the facility are denominated in British pounds and their
   aggregate face amount will fluctuate based on exchange rates. The credit facility expires on March
   31, 2011. At June&amp;#160;30, 2010, letters of credit with an aggregate face amount of $122.7&amp;#160;million were
   outstanding under the credit facility.
   &lt;/div&gt;
   &lt;div align="justify" style="font-size: 10pt; margin-top: 10pt"&gt;This credit facility contains customary covenants for facilities of this type, including
   restrictions on indebtedness and liens, limitations on mergers, dividends and the sale of assets,
   and requirements as to maintaining certain consolidated tangible net worth, statutory surplus and
   other financial ratios. The credit facility also provides for customary events of default,
   including failure to pay principal, interest or fees when due, failure to comply with covenants,
   any representation or warranty made by the Company being false in any material respect, default
   under certain other indebtedness, certain insolvency or receivership events affecting the Company
   and its subsidiaries, the occurrence of certain material judgments, or a change in control of the
   Company. The letter of credit facility is secured by a pledge of the stock of certain insurance
   subsidiaries of the Company. To the extent the aggregate face amount issued under the credit
   facility exceeds the commitment amount, we are required to post collateral with the lead bank of
   the consortium. We were in compliance with all covenants under the credit facility at June&amp;#160;30,
   2010.
   &lt;/div&gt;
   &lt;div align="justify" style="font-size: 10pt; margin-top: 10pt"&gt;As a result of the April&amp;#160;1, 2010 amendment of the credit facility, the applicable margin and
   applicable fee rate payable under the letter of credit facility are now based on a tiered schedule
   that is based on the Company&amp;#8217;s status as determined from its then-current ratings issued by S&amp;#038;P and
   Moody&amp;#8217;s Investors Service (&amp;#8220;Moody&amp;#8217;s&amp;#8221;) with respect to the Company&amp;#8217;s senior unsecured long-term debt
   securities without third-party credit enhancement.
   &lt;/div&gt;
   &lt;/div&gt;
</NonNumbericText>
          <NonNumericTextHeader>&lt;!--DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd" --&gt;
   &lt;!-- Begin Block Tagged Note</NonNumericTextHeader>
          <FootnoteIndexer />
          <hasSegments>false</hasSegments>
          <hasScenarios>false</hasScenarios>
          <DisplayDateInUSFormat>false</DisplayDateInUSFormat>
        </Cell>
      </Cells>
      <OriginalInstanceReportColumns />
      <ElementDataType>us-types:textBlockItemType</ElementDataType>
      <SimpleDataType>textblock</SimpleDataType>
      <ElementDefenition>Credit Facility Text Block.</ElementDefenition>
      <ElementReferences>No authoritative reference available.</ElementReferences>
      <IsTotalLabel>false</IsTotalLabel>
    </Row>
  </Rows>
  <Footnotes />
  <NumberOfCols>1</NumberOfCols>
  <NumberOfRows>2</NumberOfRows>
  <HasScenarios>false</HasScenarios>
  <MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel>
  <SharesRoundingLevel>UnKnown</SharesRoundingLevel>
  <PerShareRoundingLevel>UnKnown</PerShareRoundingLevel>
  <HasPureData>false</HasPureData>
  <SharesShouldBeRounded>true</SharesShouldBeRounded>
</InstanceReport>
