Not included due to lack of space:
Gene Vincent (more popular in Europe than in the USA)
Everly Brothers (influential, but more pop than rock & roll)
Lonnie Donegan (not really a rock & roller)......
Little Richard would be my 2nd choice. As well as influencing soul singers like James Brown & Otis Redding, he was also a big influence on hard rock singers like Robert Plant, Noddy Holder & Ian Gillan (& Macca too!).
Bill Haley was the first rock & roller to have mass success outside the "rhythm & blues" charts, & without him it's doubtful that Elvis & all the others would've got on TV. I don't think he was very influential beyond this though.
Elvis Presley was the first rock (& roll) superstar, & inspired a great many to pick up a guitar for the first time. I still think both Chuck & Richard were more influential though, at least in ROCK (as opposed to pop singers).
Jerry Lee Lewis is my personal fave, but I think his influence has been more in his attitude rather than music (though both Tom Jones & Cliff Richard cite him as a major influence). The main reasons he hasn't been more influential is because he plays piano (& not guitar), & he's rarely written his own material.
Buddy Holly showed everyone how to do something a bit different with 3 or 4 chords, & also proved that you didn't have to look like a rock star to be a success.
Fats Domino was a big influence on ska & blue beat in Jamaica, which later led to reggae of course. So without Fats Domino we probably wouldn't have The Police! ; )
Bo Diddley, as well as many people imitating his most famous "beat", he was a pioneer in introducing weird effects into his guitar playing.
Carl Perkins was more or less just a one hit wonder, but without him George Harrison's playing would've sounded very different, & so would John Fogerty's!
Eddie Cochran's songs & sound can be heard in heavy rock, glam & punk, & he is arguably the 2nd-most influential guitarist on this list.
But my number one choice is Chuck Berry, as his influence can be heard in everyone from The Beach Boys to Led Zeppelin to The Sex Pistols to Oasis & beyond, & it's impossible to imagine rock music without his contribution!