From the TSA website about traveler dress:

"Outer coats including trench coats, ski jackets, leather jackets, overcoats and parkas must go through the X-ray machine for inspection. If you choose to wear an outer coat to the checkpoint, you will need to either place it in your carry-on or put it in the bin that is provided for you. You will not need to remove suit jackets or blazers unless requested by the screener."

It sounds like you need to be able to take the "suit" off at security if asked.