1959, which I kind of consider being born in the sixties, since by the time I was old enough to be cognizant, it was the sixties. On the other hand, many might not consider the sixties to have officially begun until 1964, when the Beatles first landed in America...
The song at the top of the charts was "Come Softly to Me" by the Fleetwoods (not to be confused with Fleetwood Mac, who came much later).
NASA selected the Mercury Seven astronauts, Hawaii was about to become a state, The Dalai Lama Fled Tibet, Early Rock stars Richie Havens, Buddy Holly & the Big Bopper died in a plane crash, The US and USSR agreed that Antarctica would thereafter be a scientific preserve and both Barbie and The Twilight Zone debuted, and the best picture Oscar went to (yawn) Gigi).
I'm as old as The Twilight Zone. Kewl.