by chance: occasionally,incidentally,accidentally occasionally: on a few occasions <occasionally she'll walk instead of drive> incidentally: 1) by chance <in this discussion grave questions were brought up incidentally> 2) by way of interjection or digression <another leading industry, incidentally, has quadrupled its business in four years> accidentally : arising from extrinsic causes, accidental, fortuitous, casual, contingent mean not amenable to planning or prediction.

Hi sunshine, Incidentally and accidentally can mean the same thing, but accidentally usually also means something happening you didn't mean to. Incidentally and by chance generally mean the same thing :) Umm...hmm...Incidentally can also be used as a transition in (spoken) thought, a segue; just as "As it turned out,..." can be. Occasionally is something that happens repeatedly throughout time at different intervals (hours, days, weeks, months, etc). Something that...happens "every now and then". These are hard for me to explain but I hope I helped. :-D ~_~. Maidhc