A photograph of two women walking topless, along with the claim that the image showed a young Hillary Clinton and her "LGBT roommate of four years" was recirculated on the internet in October 2016:
It's not entirely clear which of the women is supposed to be Hillary Clinton and which is supposed to be her former roommate, but neither bears more than a passing resemblance to a young Hillary Rodham:
The image was taken near San Francisco State College in California, across the country from Wellesley College in Massachusetts (where Clinton attended).
Gene Anthony took the photograph in 1966:
Two women stroll topless near San Francisco State College. The women were protesting the fact that people were suggesting a law demanding women wear bras at a time when hippie women were beginning to shed them.
It's unclear why a topless photograph of the Democratic presidential nominee would only surface fifty years later, in October 2016. During her time at Wellesley, Clinton was head of the Young Republicans Club and an intern in D.C., and it is unlikely that she would have taken the time to fly to San Francisco with her roommate for a stroll around the block with her top off.
Actual photographs of Clinton during her college years do exist; however, the image displayed here is not one of them.