Well, for starters, Rock and Roll came from previous genres of music, so sometimes its difficult to draw the line of what is rock and what is something else (the Saxophone, for example, was an early intrument used that would never be used in modern rock, but reflects the roots from jazz). Like Jazz, boogie woogie, and rhythm and blues, which were originated predominantly by African American groups. However, at the same time, country music inspired people like Bill Haley (who wrote "Rock Around the Clock", which is the first number 1 rock record) and Elvis Presley (Bill Haley was listed as a Country Western musician when they didn't know what to call him).
A lot of people came out at the same time as Elvis, so it isn't really fair to single out Elvis as first. It can be argued, however, that rock and roll goes back all the way to the 40s, with people like Fats Domino, who definately have a rock and roll style.
EDIT: I read a little more into it to refresh my memory. Rolling Stones magizine considers Elvis to have the first rock and roll album, so I suppose its more of a matter of opinion of who is first, rather than any kind of consensus whatsoever.