Synonyms for By Chance (same or very similar meaning)
WordNet sense 1 (through chance):
perchanceWordNet sense 2 (by accident):
haply, by luckWordNet sense 3 (in an incidental manner):
accidentally, incidentallyWordNet sense 4 (without advance planning):
circumstantially, unexpectedlyFrom the ODE community, based on WordNetadd/edit