Exhibit 31.1

CERTIFICATION PURSUANT TO SECTION 302 
OF THE SARBANES-OXLEY ACT OF 2002

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|I, Daniel J.
 Starks, certify that:
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|                                    | 1. | I have
 reviewed this annual report on Form 10-K of St. Jude Medical, Inc.;                                                                                                                                                                                                                                                              
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|                                    | 2. | Based on my
 knowledge, this report does not contain any untrue statement of a material
 fact or omit to state a material fact necessary to make the statements made,
 in light of the circumstances under which such statements were made, not
 misleading with respect to the period covered by this report;                           
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|                                    | 3. | Based on my
 knowledge, the financial statements, and other financial information included
 in this report, fairly present in all material respects the financial
 condition, results of operations and cash flows of the registrant as of, and
 for, the periods presented in this report;                                              
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|                                    | 4. | The
 registrants other certifying officer and I are responsible for establishing
 and maintaining disclosure controls and procedures (as defined in Exchange
 Act Rules 13a-15(e) and 15d-15(e)) and internal control over financial
 reporting (as defined in Exchange Act Rules 13a-15(f) and 15d-15(f)) for the
 registrant and have:
|                                    |    |                                                                                                                                                                                                                                                                                                                                           |                                                                                                                                                                                                                                                                                                                                                                                             
|                                    |    | a)                                                                                                                                                                                                                                                                                                                                        | Designed
 such disclosure controls and procedures, or caused such disclosure controls
 and procedures to be designed under our supervision, to ensure that material
 information relating to the registrant, including its consolidated
 subsidiaries, is made known to us by others within those entities,
 particularly during the period in which this report is being prepared;         
|                                    |    |                                                                                                                                                                                                                                                                                                                                           |                                                                                                                                                                                                                                                                                                                                                                                             
|                                    |    | b)                                                                                                                                                                                                                                                                                                                                        | Designed
 such internal control over financial reporting, or caused such internal
 control over financial reporting to be designed under our supervision, to
 provide reasonable assurance regarding the reliability of financial reporting
 and the preparation of financial statements for external purposes in
 accordance with generally accepted accounting principles;                
|                                    |    |                                                                                                                                                                                                                                                                                                                                           |                                                                                                                                                                                                                                                                                                                                                                                             
|                                    |    | c)                                                                                                                                                                                                                                                                                                                                        | Evaluated
 the effectiveness of the registrants disclosure controls and procedures and
 presented in this report our conclusions about the effectiveness of the
 disclosure controls and procedures, as of the end of the period covered by
 this report based on such evaluation; and                                                                                                     
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|                                    |    | d)                                                                                                                                                                                                                                                                                                                                        | Disclosed in
 this report any change in the registrants internal control over financial
 reporting that occurred during the registrants most recent fiscal quarter
 (the registrants fourth fiscal quarter in the case of an annual report) that
 has materially affected, or is reasonably likely to materially affect, the
 registrants internal control over financial reporting; and
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|                                    | 5. | The
 registrants other certifying officer and I have disclosed, based on our most
 recent evaluation of internal control over financial reporting, to the
 registrants auditors and the audit committee of the registrants board of
 directors (or persons performing the equivalent functions):                                      
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|                                    |    | a)                                                                                                                                                                                                                                                                                                                                        | All
 significant deficiencies and material weaknesses in the design or operation
 of internal control over financial reporting which are reasonably likely to
 adversely affect the registrants ability to record, process, summarize and
 report financial information; and                                                                                                               
|                                    |    |                                                                                                                                                                                                                                                                                                                                           |                                                                                                                                                                                                                                                                                                                                                                                             
|                                    |    | b)                                                                                                                                                                                                                                                                                                                                        | Any fraud,
 whether or not material, that involves management or other employees who have
 a significant role in the registrants internal control over financial
 reporting.                                                                                                                                                                                                               

|                                                 | 
|------------------------------------------------ | 
|Date: February
 27, 2009                         | 
|                                                 | 
|/s/   DANIEL J. STARKS                           | 
|Daniel J. Starks                                 | 
|Chairman, President and Chief Executive
 Officer | 

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