The Mysterious 10th Bearer.

[Boromir88]

I've dug up the exact quote from "Many Meetings." The page won't do any good since there are many different editions. It is right around the part when Bilbo asks Frodo if he could see the ring.

LOTR: Many Meetings
When he had dressed, Frodo found that while he slept the Ring had been hung about his neck on a new chain.