I remember that well, even though the only place I ever heard it was on Junior Choice rather too many years ago. I think it came out in 1962 (which predates me, before the smartassed comments fly in). One thing I learnt today while Googling this one is that Barry McGuire, who had a one-hit wonder with the very fine Eve Of Destruction, was a member of the New Christy Minstrels who were the performers of Three Wheels On My Wagon.
Information you never wanted to know, but that's the joy of Answerbank.