c. 1300, chymbe "a cymbal," from Old French chimbe or directly from Latin cymbalum (see cymbal, the modern word for what this word originally meant). Old English had cymbal, cimbal in the "cymbal" sense. Evidently the word was shortened in Old French then misinterpreted in Middle English as chymbe bellen (a form also attested from c. 1300) and its sense shifted to "set of bells in a church or clock tower, apparatus or arrangement for striking bells," which is attested from mid-15c. Meaning "set of bells tuned to a musical scale" is from 1560s.
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.