1560s, from Latin chorus "a dance in a circle, the persons singing and dancing, the chorus of a tragedy," from Greek khoros "band of dancers or singers, dance, dancing ground," perhaps from PIE *gher- "to grasp, enclose," if the original sense of the Greek word is "enclosed dancing floor." Extension from dance to voice is because Attic drama arose from tales inserted in the intervals of the dance. In Attic tragedy, the khoros (of 15 or 24 persons) gave expression, between the acts, to the moral and religious sentiments evoked by the actions of the play.
Originally in English used in theatrical sense; meaning of "a choir" first attested 1650s. Meaning "the refrain of a song" (which the audience joins in singing) is 1590s. As a verb, 1703, from the noun. Chorus girl is 1894.