This took me by surprise, I had no idea of the connection. (As always OED is my source.)
chance, n., adj. and adv.
Etymology: Middle English chea(u)nce , < Old French cheance (= Provençal cazensa , Italian cadenza ) < late Latin cadentia falling, < cadent- falling, present participle of cadĕre to fall: compare cadence n.
Falling. Of course! It makes perfect sense. It still amazes me that one can use a word all one’s life and never suspect its origin. Apologies to those who were already aware of this.