**Exhibit 31.1**CERTIFICATION OF CHIEF EXECUTIVE OFFICERI, Lukas Braunschweiler, certify that:1. I have reviewed this Annual Report on Form 10-Q of Dionex Corporation; 2. Based on my knowledge, this report does not contain any untrue statement of a material fact oromit to state a material fact necessary to make the statements made, in light of the circumstances under which suchstatements were made, not misleading with respect to the period covered by this report. 3. Based on my knowledge, the financial statements, and other financial information included inthis report, fairly present in all material respects the financial condition, results of operations and cash flows of theregistrant as of, and for, the periods presented in this report; 4. The registrant’s other certifying officer(s) and I are responsible for establishing andmaintaining disclosure controls andprocedures (as defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) and internal controlover 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 controlsand procedures to bedesigned under the Company’s supervision, to ensure that material information relating to theregistrant, 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 internalcontrol over financial reporting to be designed under the Company’s supervision, to providereasonable assurance regarding the reliability of financial reporting and the preparationof financial statements for external purposes in accordance with generally acceptedaccounting principles;  (c) Evaluated the effectiveness of the registrant’s disclosure controls and procedures andpresented in this report the Company’s conclusions about the effectiveness of thedisclosure controls and procedures, as of the end of the period covered by this reportbased on such evaluation; and  (d) Disclosed in this report any change in the registrant’s internal control over financialreporting that occurred during the registrant’s most recent fiscal quarter (theregistrant’s fourth fiscal quarter in the case of an annual report) that has materiallyaffected, or is reasonably likely to materially effect, the registrant’s internal controlover financial reporting; and5. The registrant’s other certifying officer(s) and I have disclosed, based on the Company’smost recent evaluation of internal control over financial reporting, to the registrant’sauditors and the audit committee of registrant’s board of directors (or persons performingthe equivalent functions): (a) All significant deficiencies and material weaknesses in the design or operation ofinternal control over financial reporting which are reasonably likely to adversely affectthe 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 whohave a significant role in the registrant’s internal control over financial reporting.Date: November 9, 2005   /s/ Lukas Braunschweiler     Lukas Braunschweiler  President, Chief Executive Officer and Director