In Administrative, Procedural, and Miscellaneous Notice 2004-50, the IRS addresses this question. See Questions 2 and 4, excerpted below:
 Q-2. May an otherwise eligible individual who is eligible for Medicare, but not enrolled in Medicare Part A or Part B, contribute to an HSA?
 A-2. Yes. Section 223(b)(7) states that an individual ceases to be an eligible individual [...]

Employees who are enrolled in the High Deductible Health Plan (HDHP) are eligible to contribute to an HSA.  The employee can not be enrolled in any other health plan coverage that provides medical benefits before the HDHP deductible is met, not claimed as dependent under someone else’s tax return, and not enrolled in Medicare.

Normally, you are permitted to contribute 1/12th of your annual maximum for each FULL month you are covered by the HDHP.  For example if you have single coverage and are covered for 6 of 12 months in the TAX year, you may contribute 6/12ths of the annual maximum of $2900 (in 2008) or $1,450. Some [...]