If it was Chubby Checker, the B sides were probably something like Peppermint Twist and Let’s Twist Again. 
He used to show up at the Milwaukee Summerfest almost every year. He could really get the crowd going. Fun stuff.
Good call ccwaterback. 1960 was “Toot Toot” & 1961 was AFAIK “Twistin USA” or some similar. Actually “Let’s Twist Again” in mid 1961 helped get the “twist craze” started in late 1961. Joey Dee sang Peppermint Twist. Joe Pesci as a kid was in Dee’s movie about the twist.
Didn’t Del Shannon “cover” the Beatles’ From Me to You, but before the tune was released in the USA? Don’t know if Shannon’s version made it to Top Ten.
Yes he did. He asked them if he could record it after he heard it at a concert in England, where the Beatles opened for him. It charted at about #75 for Del. It was out in mid 1963- just around the time the Beatles Vee Jay album "Please Please Me "came out. It is very close whose version was 1st- but his charted in US in 1963, theirs did not until 1964.
Hey, Doc, you are on it!
What about that treacly Marianne Faithful/Stones tune, As Tears Go By?