na-adjective, noun which may take the genitive case particle 'no', noun
unexpected meeting; coincidence
Used when meeting someone by chance, often with a sense of pleasant surprise. Commonly appears in phrases like 奇遇ですね (What a coincidence!).
What a coincidence meeting you here!
It's a coincidence that I'm staying at the same hotel as him.
What a coincidence to meet you in a place like this!
By a strange coincidence, she turned out to be my childhood friend.
巡り合わせ suggests fate or a twist of destiny bringing things together, whereas 奇遇 focuses narrowly on a surprising chance encounter with someone.
From 奇 (strange, unusual) and 遇 (meeting, encounter). The exact historical derivation is uncertain, but the kanji combination directly suggests an unusual encounter.