Only one of the original Nazi Party was openly gay. His name was Ernst Rohm, and he was the leader of the S.A. or Brownshirts. Hitler authorized Heinrich Himmler to murder Rohm during the Night of the Long Knives in 1934.
Lothar Machtan, a German history professor, in a book called "the Hidden Hitler" claims that Hitler and Rudolf Hess were gay lovers in prison during the 1920s. This, however, is highly controversial and impossible to prove with the existing historical evidence.