Chorus is Greek khoros through Latin, and the ch says k because it transliterates the Greek letter chi. The Greek word meant a round dance, then the dancing-place, then the band of dancers, and finally the company of performers in a play who comment on the action between the acts. The extension from dancing to singing happened because Attic drama grew out of stories told in the intervals of the dance — the singers were the dancers.
English took it in the 1560s in the narrow dramatic sense: the figure who speaks the prologue and explains the events on stage. The musical senses followed. What the Greek word originally meant is genuinely unknown; the guesses run to "enclosed dancing floor" or "to rejoice," neither certain. It is a useful reminder that even the most confidently classical-looking word can have an opaque bottom.
chorus (n.) 1560s, in drama, "person who speaks the prologue and explains or comments on events on stage," from Latin chorus "a dance in a circle, the persons singing and dancing, the chorus of a tragedy," from Greek khoros "round dance; dancing-place; band of dancers; company of persons in a play, under a leader, who take part in dialogue with the actors and sing their sentiments at intervals." The Greek word is of uncertain origin, because the original sense is unknown. Perhaps it is from PIE root *gher- (1) "to grasp, enclose," if the original sense of the Greek word is "enclosed dancing floor," or *gher- (2) "to like, want," if the original notion is "to rejoice." 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 12 or 15 (tragic) or 24 (comedic) persons) gave expression, between the acts, to the moral and religious sentiments evoked by the actions of the play. English 16c. theater adopted a stripped-down version of this. When a Poet wished to bring out a piece, he asked a Chorus from the Archon, and the expenses, being great, were defrayed by some rich citizen (the khoregos ): it was furnished by the Tribe and trained originally by the Poet himself [Liddell & Scott] The meaning "an organized company of singers" is from 1650s. Meaning "the refrain of a song" (which the audience joins in singing) is from 1590s; that of "a song to be sung by a (large) chorus" is from 1744. In reference to the main part of a modern popular song (as distinguished from the verse , q.v.), by 1926, originally in jazz. As a verb, 1703, from the noun. Chorus girl "young woman who sings and dances in a stage chorus" is attested by 1852. also from 1560s