WordNet (r) 3.0 (2006):

happenstance
    n 1: an event that might have been arranged although it was
         really accidental [syn: coincidence, happenstance]

Moby Thesaurus II by Grady Ward, 1.0:

86 Moby Thesaurus words for "happenstance":
   accessory, accident, accidental, accidentality,
   actuarial calculation, addendum, addition, adjunct,
   adventitiousness, adventure, appendage, appurtenance, auxiliary,
   break, casualness, casualty, chance, chance hit, circumstance,
   collateral, contingency, contingent, destiny, episode, event,
   experience, extra, fact, fate, fluke, flukiness, fortuitousness,
   fortuity, fortune, freak accident, gamble, good fortune, good luck,
   hap, happening, happy chance, hazard, heedless hap, how they fall,
   incident, incidental, indeterminacy, indeterminateness,
   inessential, law of averages, long odds, long shot, lot, luck,
   lucky shot, matter of fact, mere chance, moira, nonessential,
   not-self, occasion, occurrence, opportunity, other, particular,
   phenomenon, principle of indeterminacy, probability,
   problematicness, random sample, reality, risk, run of luck,
   secondary, serendipity, statistical probability, subsidiary,
   superaddition, supplement, the breaks, theory of probability,
   turn of events, uncertainty, uncertainty principle, unessential,
   whatever comes