At about 10:59 eastern time, a Piper PA-32-300 had both main landing gear brakes catch fire during taxi. The pilot was not injured. The pilot said he picked up the airplane from a maintenance company, taxied to the runway with a passenger and took off. Just prior to liftoff the left wheel brake appeared to grab. He flew locally and returned to the airport, where he dropped off his passenger. He again taxied to the runway to fly to Vero Beach, Fla. and felt the left brake grab again. He taxied to the end of the runway and the left brake again grabbed. He elected to return to the maintenance company. As he approached the ramp, he smelled smoke. Personnel from the maintenance company came to the airplane with fire extinguishers and put out the brake fires. The maintenance company personnel said they found the parking brake on after they put out the brake fires.