Rob, no-one else has replied yet so here's my take on them, assuming you mean in the musical context!
Don't know when the term "lick" was applied first to a short, quick phrase or sequence of notes that might be learnt and usefully recalled esp. in improvising. I'm sure it goes back to the 1920s at least. I guess it comes from other uses of a "lick" as in something flickering,or moving lightly or quickly, eg a lick of flame, or paint, or going at a bit of a lick.
I think chops is from the slang choppers, originaly meaning teeth but modified over time, probably by musicians, to include all the jaw, mouth and muscles thereof. The trained creole clarinetist Joe Darensbourg is said to have complained in the 1940s about the rediscovery of the veteran, unsophisticated, New Orleans trumpeter Bunk Johnson as a "drunk with no chops" (ie toothless, as indeed he was when found). Louis Armstrong though applied copious amounts of lip balm to, as he said, take care of his chops.
Colin