The series, starring veteran actor Jeffrey Tambor, tells the story of a man who has transitioned to become a woman and is working out the thorny details of telling his family.
"This is dedicated to too many trans people that died too young," said series creator Jill Soloway.
"Maybe we'll be able to teach the world something about authenticity and truth and love." In October, Amazon ordered a second season of the series - the creation of Soloway, an Emmy-nominated writer on cult series "Six Feet Under."
The first season was released on September 26.
Amazon has recently bolstered its streaming video offerings.
But so far, its own original content has not quite reached the popularity level achieved by Netflix, with its signature series "House of Cards" and "Orange Is The New Black."