on the outside chance
Because there is a very slight, remote, or unlikely possibility (that something may happen or be the case). (A less common variant of "on the off chance.") You'll probably need to replace your washing machine, but on the outside 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 outside chance that he says yes, I'm going to ask him anyway!