The story
hap (“luck, fortune, chance”) + chance (“chance, fortune”): a tautological compound, in which both elements independently mean “chance”. Compare the similarly redundant haphazard (hap + hazard), and the synonymous happenchance and happenstance. Recorded from 1866, but attested chiefly in literary prose of the 20th century.
Etymology from Wiktionary, CC BY-SA 4.0.