우연(n) is the most common word for "coincidence". 우연한 (coincidental, accidental) is the adjective and 우연히, 우연하게 the adverbs (by chance, by coincidence). In Korean there seems to be no simple dominant expression like "What a coincidence!" but a few different ones. 1. 이런 (기막힌) 우연이 있나! This is such a (amazing) coincidence!. 2. (참) 묘한 [이상한, 재미있는] 우연이네. This is a fascinating [strange, interesting] coincidence. 3, 아, 이런 우연이! Ah, what a coincidence! 4. 호랑이도 제 말하면 온다더니! Speak of the devil! (When someone you mentioned shows up by chance). There are also 공교롭다(adj) and 공교로이, 공교롭게(adv), but they have a narrower usage than 우연한, 우연하다, 우연히. 우연한 means any occurrence that wasn't planned or anticipated, while 공교로운 refers to those much less probable. - 어느 날 출근 길에 우연히 만난 사람: Someone I met by chance on my way to work. - 어느 날 출근 길에 공교로이 만난 사람: (sounds very weird) - 공교롭게도 그는 그날 결근을 했다: It so happened that he missed work that day. - 공교로운 것은 앙숙인 두 정치인이 같은 고향 출신이라는 것이다: What's coincidental is that the two fiercely antagonistic politicians hail from the same hometown.