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1868, American English abbreviation of champion (n.).
"to chew noisily," 1520s, probably echoic; OED suggests a connection with jam (v.). Earlier also cham, chamb, etc. To champ on (or at) the bit, as an eager horse will, is attested in figurative sense by 1640s. Related: Champed; champing. As a noun in this sense, attested from c.1600.
To be eager or enthusiastic: champing at the bit to run the race (mid-1600s+)
To be eager for action; be impatient: He'd been chomping at the bit real hard the last three weeks (1640s+)