We know the Rolling Stones’ first hit single was “I want to be your man”, written by L-M. But how true is the legend that Mick caught the two aboard a moving train and buttonholed them into writing a song for him? It must have been a desperate move ("Hey guys, how about song, eh? Been in this __ years now and still no hit single.) Lennon-McCartney were said to have obliged him cheerfully and wrote the song in ten minutes.
Never heard this story. I have heard that Paul has said that he would have loved to have written “Satisfaction”. Satisfaction is very much in with the sound of the rest of the Rolling Stones. The Stones wrote it, pure and simple.
Read Stoned by Andrew Loog Oldham - their manager at the time. He worked for the Beatles and left to manage The Stones. He was the one forcing Mick and Keith to write - they didn’t want to. The Stones were in the studio coming up dry and Oldham stepped out. He saw L&M on the street and was talking with them, expressing desire for M&K to start writing. They said they had a half written song they’d be happy to share. They came in, played a verse and chorus, and the Stones said they liked it, so L&M went off to a corner of the studio to finish it, embarrassing the Stones but also inspiring them…
You’re welcome 
Thanks. “Come on” was the first single (made #21.) “I want to be your man” by L-M was the second and reached #12. The third was “Not fade away” which hit #3.
When I read this, my head automatically went to:
Some variation of this story appears in every history of the Stones, and that must be thousands.
To be fair, I’ve also never heard the version of the story given in the OP. The version I know matches the one given by WordMan: it was Oldham, not Jagger, who collared the Fab Two, and no train was involved.
I’ve read lots of variations. L&M had the song written out; they didn’t have any song; they had half a song. They wrote it on the spot; they went home and returned the next day. They happened to be there; they were bumped into; they were phoned.
No train, true, but The Second Stone seemed to be unfamiliar with any version, especially when throwing in the completely unrelated “Satisfaction,” which was… odd.
No biggie. Just the way it was phrased struck my funny bone.
There were 2 recent articles about the Stones’ relationship with the Beatles recently in Slate.com’s “Blogging the Beatles feature.”
The Beatles give their songs away and
When the Beatles met the Rolling Stones