by chance 偶然；碰巧;意外地

【例句】
Several years after they'd split up they met again by chance in Paris.
他们分手几年以后在巴黎又碰巧相遇。

The pair met often — at first by chance but later by design.
这两个人经常见面——开始是偶然的，后来就是有意的了。