1620s, a more recent variant of hiccup (q.v.) by mistaken association with cough.
Entries linking to hiccough
hiccup n.
1570s, hickop, earlier hicket, hyckock, "a word meant to imitate the sound produced by the convulsion of the diaphragm" [Abram Smythe Palmer, "Folk-Etymology," London, 1882]. Compare French hoquet, Danish hikke, Persian hikuk, Hindi hichki, etc. Modern spelling first recorded 1788; An Old English word for it was ælfsogoða, so called because hiccups were thought to be caused by elves.