Adela Hernandez is a biologically male Cuban who has lived as a female since childhood.
She calls her election an important advance for rights to sexual diversity.
In decades past, Cuban authorities persecuted gay people and others seen as threatening to the revolution. Many were sent to grueling work camps in the countryside.
Hernandez was jailed for two years in the 1980s for "dangerousness."
But there has been a shift away from macho attitudes in recent years after Fidel Castro himself expressed regret over past treatment of gays.
(Copyright 2012 by The Associated Press. All Rights Reserved.)