Lucille Ball, as many of you picked up on.
The photo, which is absolutely authentic - it comes from Stefan Kanfer's book Ball of Fire , dates from the early 1930s (1932 or '33 probably - my ability to check a reference was hurt by the fact that the Public Library was closed today) either during her period as a model for designer Hattie Carnegie, or her period as a Goldwyn Girl. She was about 21 at the time, and probably a blonde. Lucy started in movies (including Roman Scandal where she played a "naked" slave girl) in 1933 and she soon became known as the "Queen of the Bs" at RKO and later at MGM. She was 40 years old when I Love Lucy debuted and made two movies, The Long, Long Trailer and Forever Darling with her husband and business partner Desi Arnaz during hiatuses in the production of I Love Lucy, as well as other movies during breaks from her later series. Besides producing both I Love Lucy and the later Lucy Show (the first season of which was produced by Desi), Desilu Studios produced such series as December Bride, The Untouchables, Star Trek, Mission Impossible, and Mannix. When Desi Arnaz sold his interest in the studio to Lucy she became the first woman to head a major Hollywood studio.
As for those of people who described seeing this photo as being "like seeing your grandma naked when she was young" (as Sam Johnson put it) consider that a woman of 20 who posed in Playboy in 1960 would be 65 years of age and probably has grandchildren between 15 and 20. The difference is that Lucy was in the public eye a lot more - and a lot longer - than virtually any woman who has been a Playboy centerfold. More over most of us became aware of her when she was at an age when most women her age would have been grandmothers. And if you really want to be grossed out, consider that Shirley Jones, at nearly 72, has a bedroom scene in the new Adam Sandler movie Grandma's Boy. Now that's an EWWW moment.