Military aircraft from three South American countries were scouring the turbulent waters of the South Atlantic north of Antarctica on Tuesday after a Chilean Hercules C-130 military transport plane disappeared the night before with 38 people aboard.

Air-traffic controllers lost contact with the aircraft about an hour and a half after it left a Chilean air base in Punta Arenas, the capital of Chile’s southernmost region, and flew over the Drake Passage en route to a Chilean air strip on King George Island off the Antarctic...