chap: There are four distinct words chap in English. The oldest, ‘sore on the skin’ , originally meant more generally ‘crack, split’, and may be related to Middle Low German kappen ‘chop off’; it seems ultimately to be the same word as chop ‘cut’. Chap ‘jaw’  (as in Bath chaps) is probably a variant of chop (as in ‘lick one’s chops’). Chap ‘fellow’  originally meant ‘customer’; it is an abbreviation of chapman ‘trader’ [OE] (source of the common surname, but now obsolete as an ordinary noun), whose first element is related to English cheap. Chaps ‘leggings’  is short for Mexican Spanish chaparreras, a derivative of Spanish chaparro ‘evergreen oak’; they were named from their use in protecting the legs of riders from the low thick scrub that grows in Mexico and Texas (named with another derivative of chaparro, chaparral). Chaparro itself probably comes from Basque txapar, a diminutive of saphar ‘thicket’. => chop; cheap; chaparral
"to crack," mid-15c., chappen (intransitive) "to split, burst open;" "cause to 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." Related: Chapped; chapping. The noun meaning "fissure in the skin" is from late 14c.