Mid 18th century; earliest use found in The London Magazine. From Poll + parrot.
1To chatter like a parrot; to talk incessantly or inconsequentially, to prattle.
2rare To talk repetitively or without pause to (a person). Also (with away): to spend (time) in idle or repetitive talk.
Mid 19th century; earliest use found in Charles Dickens (1812–1870), novelist. From poll-parrot.