chap (n.)

1570s, "customer," short for obsolete chapman in its secondary sense "purchaser, trader" (also see cheap). Colloquial familiar sense of "lad, fellow, man or boy" is first attested 1716, usually with a qualifying adjective. Compare slang (tough) customer and German Knude "customer, purchaser," colloquially "fellow."

chap (v.)

"to crack open in fissures," mid-15c., chappen (intransitive) "to split, burst open in fissures;" "cause to split or crack" (transitive); perhaps a variant of choppen (see chop (v.), and compare strap/strop), or related to Middle Dutch kappen "to chop, cut," Danish kappe, Swedish kappa "to cut."

Usually in reference to the effects of extreme cold followed by heat on exposed body parts. Related: Chapped; chapping. The noun meaning "fissure in the skin" is from late 14c.