on the chance that

In the (usually unlikely) possibility (that something may happen or be the case). You'll probably need to replace your washing machine, but on the chance that I can fix it, let me open it up and take a look. I don't think Jack would go on a date with me, but on the chance that he says yes, I'm going to ask him anyway!

On the possibility that, as in I came early on the chance that we might have time to chat. This phrase uses chance in the sense of "a possibility or probability for some event," a usage dating from the late 1700s. It is sometimes put as on the off chance, meaning "on the slight but unlikely possibility," as in I came late on the off chance that I could avoid Thomas. The addition of off in the sense of "remote" dates from the mid-1800s.