UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

WASHINGTON, D.C. 20549

SCHEDULE 13G

UNDER THE SECURITIES EXCHANGE ACT OF 1934

(AMENDMENT NO. __)

STEMCELLS, INC.

(Name of Issuer)

COMMON STOCK, $0.001 PAR VALUE

(Title of Class of Securities)

85857R105

-

(CUSIP Number)

December 21, 2011

(DATE OF EVENT WHICH REQUIRES FILING OF THIS STATEMENT)

Check the appropriate box to designate the rule pursuant to which this Schedule is filed: [X] Rule 13d-1(c)

*The remainder of this cover page shall be filled out for a reporting person's initial filing on this form with respect to the subject class of securities, and for any subsequent amendment containing information which would alter the disclosures provided in a prior cover page.

The information required in the remainder of this cover page shall not be deemed to be "filed" for the purpose of Section 18 of the Securities Exchange Act of 1934 ("Act") or otherwise subject to the liabilities of that section of the Act but shall be subject to all other provisions of the Act (however, see the Notes).

(Continued on following page(s)

Page 1 of 4 Pages

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CUSIP No. 85857R105     13G    Page 2 of 4 Pages

 1.     NAMES OF REPORTING PERSON

                S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

              Alpha Capital Anstalt

2.      CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP:

                                                                 (a)   [_]

                                                                 (b)   [_]

3.      SEC USE ONLY

4.      CITIZENSHIP OR PLACE OF ORGANIZATION

Liechtenstein

5.      SOLE VOTING POWER, NUMBER OF SHARES BENEFICIALLY OWNED BY EACH REPORTING PERSON – 1,687,242 Common Stock

6.      SHARED VOTING POWER - None

7.      SOLE DISPOSITIVE POWER – 1,687,242 shares of Common Stock

8.      SHARED DISPOSITIVE POWER – None

9.     AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON -

1,687,242 shares of Common Stock

10.    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES

         CERTAIN SHARES                                                   [   X   ]

Excludes exercise of Warrants held by Alpha Capital Anstalt which Warrants contain a contractually stipulated 4.99% blocker provision.

11.    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9

7.571%

12.    TYPE OF REPORTING PERSON

CO

2

CUSIP No. 85857R105     13G    Page 3 of 4 Pages

ITEM 1 (a) NAME OF ISSUER: Stemcells, Inc., a Delaware corporation

ITEM 1 (b) ADDRESS OF ISSUER'S PRINCIPAL EXECUTIVE OFFICES:

               3155 Porter Drive, Palo Alto, CA 94304

ITEM 2 (a) NAME OF PERSON FILING: Alpha Capital Anstalt

ITEM 2 (b) ADDRESS OF PRINCIPAL BUSINESS OFFICE OR, IF NONE, RESIDENCE:

Pradafant 7, Furstentums 9490, Vaduz, Liechtenstein

ITEM 2 (c) CITIZENSHIP: Liechtenstein

ITEM 2 (d) TITLE OF CLASS OF SECURITIES: Common Stock, $0.001 par value

ITEM 2 (e) CUSIP NUMBER: 85857R105

ITEM 3 IF THIS STATEMENT IS FILED PURSUANT TO RULE 13D-1(B) OR 13D-2(B):  Not applicable

ITEM 4 OWNERSHIP

         (a) AMOUNT BENEFICIALLY OWNED: 1,687,242 Shares of Common Stock

         (b) PERCENT OF CLASS: 7.571%

         (c) NUMBER OF SHARES AS TO WHICH SUCH PERSON HAS:

             (i)   SOLE POWER TO VOTE OR DIRECT THE VOTE

                                1,687,242 Shares

             (ii)  SHARED POWER TO VOTE OR DIRECT THE VOTE

                                    0 Shares

             (iii) SOLE POWER TO DISPOSE OR TO DIRECT THE DISPOSITION OF

                                1,687,242 Shares

             (iv) SHARED POWER TO DISPOSE OR TO DIRECT THE DISPOSITION OF

                                    0 Shares

3

CUSIP No. 85857R105     13G    Page 4 of 4 Pages

ITEM 5 OWNERSHIP OF FIVE PERCENT OR LESS OF A CLASS

                                 Not applicable

ITEM 6 OWNERSHIP OF MORE THAN FIVE PERCENT ON BEHALF OF ANOTHER PERSON

                                 Not applicable

ITEM 7 IDENTIFICATION AND CLASSIFICATION OF THE SUBSIDIARY WHICH ACQUIRED THE SECURITY BEING REPORTED ON BY THE PARENT HOLDING COMPANY

                                 Not applicable

ITEM 8 IDENTIFICATION AND CLASSIFICATION OF MEMBERS OF A GROUP

                                 Not applicable

ITEM 9   NOTICE OF DISSOLUTION OF GROUP

                                 Not applicable

SIGNATURE

         After reasonable inquiry and to the best of my knowledge and belief, I certify that the information set forth in this statement is true, complete and correct.

December 21, 2011

----------------------------------------

(Date)

/s/ Konrad Ackerman

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(Signature)

Konrad Ackerman, Director

----------------------------------------

(Name/Title)

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