The official policy since about September 20 or so is that all jackets must come off unless you are wearing nothing underneath, according to the TSA website and the posters here who claim employment by the TSA.

Nevertheless, I've seen it enforced inconsistently. I've been told to remove my jacket at some checkpoints, not been told at others, and subject to secondary at some for failing to remove my jacket. Some checkpoints just let me slide with my jacket. Not too easy to get 44,000+ people to sing from the same hymnal. But at least the inconsistency keeps the terrorists off guard.