c.1300, chymbe "cymbal," from Old English cymbal, cimbal, also perhaps through Old French chimbe or directly from Latin cymbalum (see cymbal, the modern word for what this word originally meant). Evidently the word was misinterpreted as chymbe bellen (c.1300) and its sense shifted to "chime bells," a meaning attested from mid-15c.
mid-14c., chyme, from chime (n.). Originally of metal, etc.; of voices from late 14c. To chime in originally was musical, "join harmoniously;" of conversation by 1838. Related: Chimed; chiming.