This paper addresses the question of the date of appearance of Philistine Bichrome pottery at Megiddo through a new computational approach, using recently developed chronology software. Based on historical dates, we obtain a terminus post quem of 1183 B.C.E. for the start of Philistine Bichrome at Megiddo using a broad model, and a terminus post quem of 1124 B.C.E. under stronger chronological hypotheses. Adding radiocarbon results at 68.2% confidence level to the model yields a narrow range of 1111–1086 B.C.E. for the appearance of Bichrome (1128—1079 B.C.E. for 95.4%). The paper also presents results suggesting that Stratum VIIB ended during, or only slightly before, the reign of Ramesses III (1184–1153 B.C.E.).