Answer: TRUE
Historical context:
In the late 1950s, Fidel Castro led a revolution movement against Cuban dictator Fulgencio Batista. The US government had backed Batista, an example of how US foreign policy was willing to support non-democratic governments as long as they were in opposition to the threat of communism. The Cold War policies of the US in those years were all about containing and fighting against communism -- which caused problems for the US in the long run. (Heard of a thing called the Vietnam War?)
Castro's revolutionary forces were able to overtake the Batista government. Batista fled from the island on January 1, 1959 (he went to the Dominican Republic). Fidel Castro took over as communist leader of Cuba, and remained in that position into the 21st century.