They chanced to be staying at the same hotel.

他们碰巧住在同一家旅馆。

It chanced (that) they were staying at the same hotel.

碰巧他们住在同一家旅馆。

One day he chanced upon Emma's diary and began reading it.

有一天他偶然发现了埃玛的日记，便开始读了起来。

Andy knew the risks. I cannot believe he would have chanced it.

安迪知道那些风险，我不能相信他会冒那个险。