by chance vs circumstantially

by chance and circumstantially both are adverbs.

Word	Noun	Adjective	Verb	Adverb
by chance	No	No	No	Yes
circumstantially	No	No	No	Yes

As adverbs, by chance and circumstantially are synonyms defined as:

Other synonyms of by chance include accidentally, unexpectedly.

by chance (adverb)	circumstantially (adverb)
without advance planning	insofar as the circumstances are concerned
by accident	without advance planning
through chance	in minute detail
	according to circumstances