chance (v.)
late 14c., "to come about, to happen," from chance (n.). Meaning "to risk" attested from 1859. Related: Chanced; chancing.
chance (n.)
c.1300, "something that takes place, what happens, an occurrence" (good or bad, but more often bad), from Old French cheance "accident, chance, fortune, luck, situation, the falling of dice" (12c., Modern French chance), from Vulgar Latin *cadentia "that which falls out," a term used in dice, from neuter plural of Latin cadens, present participle of cadere "to fall" (see case (n.1)).

In English frequently in plural, chances. The word's notions of "opportunity" and "randomness" are as old as the record of it in English and now all but crowd out the word's original notion of "mere occurrence." Main chance "thing of most importance" is from 1570s, bearing the older sense. The mathematical (and hence odds-making) sense is attested from 1778. To stand a chance (or not) is from 1796.

To take (one's) chances "accept what happens" (early 14c.) is from the old, neutral sense; to take a chance/take chances is originally (by 1814) "participate in a raffle or lottery or game;" extended sense of "take a risk" is by 1826.