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Exhibit 31.1

CERTIFICATION PURSUANT TOSECTION 302 OF THE
SARBANES-OXLEY ACT OF 2002

I, Kenneth Hicks, certify that:

1. I have reviewed this quarterly report on Form 10-Q of
Argentex Mining Corporation;

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;

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
company as of, and for, the periods presented in this report;

4. The registrants other certifying officer(s) 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

(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;

5. The registrants other certifying officer (s) and I have
disclosed, based on my 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):

(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: December 10, 2009

|/s/ Kenneth Hicks             | 
|----------------------------- | 
|Kenneth Hicks                 | 
|President and Director        | 
|(Principal Executive Officer) | 

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