LotR -- Book 1 - Chapter 02 - The Shadow of the Past

[HerenIstarion]

Following OK implications, there are hints of the whole event being Eru's [direct?]intervention:

LoRT Book I chapter 02, Gandalf to Frodo

Behind that there was something else at work, beyond any design of the Ring-maker. I can put it no plainer than by saying that Bilbo was meant to find the Ring, and not by its maker. In which case you also were meant to have it. And that maybe an encouraging thought

meant whom by, we wonders?

More hinted at in the Unfinished Tales:

UT, Gandalf reminding himself of events preceeding There and Back Again

But that was not enough for me. I knew in my heart that Bilbo must go with him, or the whole quest would be a failure – or, as I should say now, the far more important events by the way would not come to pass.

UT, Gandalf persuading Thorin to take Bilbo along:

'Listen to me, Thorin Oakenshield !' I said. 'If this hobbit goes with you, you will succeed. If not, you will fail. A foresight is on me, aid I am warning you.'

and, finally:

But that has been averted – because I met Thorin Oakenshield one evening on the edge of spring not far from Bree. A chance-meeting, as we say in Middle-earth

Ambivalent phrase, this last one - it may imply that is was indeed by chance, but the intonation is such that it implies that what happened may seem to be a chance, but there is more to it just a bit deeper down