Hmmm. Late 1970's . . . after the creation of birth control pills but before the onset of HIV/AIDS. May be a sad statement on humanity, but the late 1970's might be a more popular destination than the birth of Christ.
Actually AIDS didn't come about till the exploration of Titan and the encounter of saturian primates. Then a time traveller took it back to 1979 hoping that a cure would be found by 2101 when he catches it.