I was pretty sure that Run DMC wasn't 'the first' (although it's hard to really define 'first' sometimes), but I was also pretty sure they predated the Beastie Boys.
It does pose an interesting question, though. Rap undoubtedly owes quite a bit to the 'speak-singing' of the late 60's and early 70's. Some of Zappa's stuff is more spoken rhyme than 'singing' (forgive me, the local Classic Rock station played something about Montana and dental floss last night.) Dylan's even a little closer to speaking than singing. Is there something that marks a composition as 'rap' that 'beat poetry' doesn't have?