Consecutive patients will be randomized on the day of admission prior to their CABG surgery into one of two groups. One group will be randomized to the placebo while the second group will receive 2.5 mg Fondaparinux Sodium injections. Both groups will receive routine mechanical prophylaxis as determined by the treating physicians. Group randomized to receive Fondaparinux Sodium will receive a 2.5 mg SQ daily drug dose starting 12 +/- 2 hours post-wound closure or the following day in the morning (at the discretion of the cardiothoracic surgeon). The second dose would be administered 24 hours later and the dosing will then be once a day. The group randomized to placebo will receive subcutaneous equivolume isotonic saline at the same time points described above.