Unwell; seedy. Generally used to describe the results of overindulgence in eating and drinking, etc. (115). Alternatively, Walters (302) thinks "chopper" refers to the ax or sword and, being cheap, is unlikely to do the work neatly, but must chip away. Rees (254) proposes that chippy means the cutting edge of the instrument is ragged (chipped). See entry for "Awry" in The Yeomen of the Guard. The following sketch is from one of Gilbert's Bab Ballads.

a cheap and chippy chopper
Act I
Bab sketch of a cheap and chippy chopper