On March 23, 2002, about 1802 eastern standard time, a Piper PA-31-325 Navaho, N49RB, registered to a private individual, doing business as Twin Air, Inc., operating as a Title 14 CFR Part 91 positioning flight, sustained a gear up landing at Hollywood-Fort Lauderdale International Airport, Florida. Visual meteorological conditions prevailed and an international visual flight plan was filed. The aircraft received minor damage, and the airline transport rated pilot, the sole occupant, was not injured. The flight originated from Marsh Harbor, Great Abaco Island, Bahamas, about 59 minutes before the incident. According to the pilot, as he entered the downwind leg for a landing on runway 09R, he asked for and received clearance from Fort Lauderdale tower to momentarily leave tower frequency to cancel his VFR flight plan with Miami AFSS. Having done so, and switching back to tower frequency, he thought he heard the tower clear him to land, but was not certain. The radio traffic was so intense that he could not get acknowledgement from the tower exactly what his interval was behind other landing traffic. He completed his landing checklist, holding the landing gear until he could confirm with the tower his clearance to land. He did not get clearance to land until he was on short final approach, and he forgot to lower the landing gear. The pilot stated he did not hear any gear warning horn at any time. A 72-hour history of the pilot's activities revealed that the 3 days prior to the incident day, (1) 9 hours 40 minutes, (2) 14 hours 55 minutes, and, (3) 8 hours 40 minutes were spent doing office work, with no flying duties. The day of the incident, the pilot was on duty for 9 hours 28 minutes, and flew 6 flight segments totaling 6 hours 55 minutes. According to the air taxi owner/operator, the pilot admitted to simply forgetting to put the gear lever down as part of his prelanding preparations. The owner, himself, was involved in the recovery of the aircraft, and stated that as soon as he placed the aircraft's "master switch" to the "on" position during the recovery, the gear warning horn sounded properly. He stated the pilot was using the full ear covering type of radio headset, and possibly he did not hear the gear warning horn.