1、We went to the cinema on the chance of seeing Paul there.
我們到電影院去，希望萬一能在那兒碰見保爾。

2、I came out here on the chance of finding you at home after all.
我到這兒來心想也許會在家找到你，沒想到竟然還真是。

3、I'll return to the station on the chance of meeting his brother.
我將回到車站期望遇到他的兄弟。

on the chance of翻譯