Panama is a village in Chautauqua County, New York, United States. The population was 479 at the 2010 census. Panama is in the northwest part of the town of Harmony, at the junction of State Route 474 and County Route 33.The village is named after Panama Rocks, a large rock formation south of the village. Paleozoic fossils are visible in the outcrops. This site has become a tourist attraction, and the owners charge admission at the gate.