Synonyms for Happenstance:

n.

coincidentally, unlucky, incidental, serendipity, stochastic, accidentally, time. certain, surprise, hap, happenchance, hazard. chance (noun)
aimlessness, purposelessness, coin toss, accident, luck, chance, fate, fluke, fortuity, incident, randomness, coincidence, haphazardness, fortune, adventure, opportunity.
circumstance (noun)
time.

Other synonyms:

happenchance. hazard, hap. Other relevant words:
hap, happenchance, hazard, incident, incidental, event, serendipity.