I was thinking of a song by the Jazz Crusaders (before the Last Poets came along), but on reflection I think there is something even earlier from around '63 by an obscure Jamaican artist. I could be stretching things a bit as both songs might be better described as proto-rap. I think the first rap (as we would recognise it today) appeared on the B-side of a Fat Back Band song in '74 (5 years before King Tim III -
http://youtu.be/UcTP4cvXSP0 - I need to dig out some more of their albums....it's been a while).
Of course there are examples of spoken rhymes over music that go back to the 20s, but there is a big difference between rapping and simply rhyming over music - some will no doubt beg to differ
.