on the (off) chance
In the unlikely event. On the off chance that you get home before me, can you put the roast in the oven?
on the chance
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 chance that
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.