on the chance that

1. 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.

Example Sentences

On the chance that he does, I have a bone to pick with him – less cosmic, but something that speaks volumes about his probity and fitness for office.

From Salon

Instead, his objective was to “twine ideas and images into big subversive pretzels of life, death and goodliness on the chance that they might help keep the world lively, and give it the flexibility to endure,” he once said.

From Los Angeles Times

You’d be betting on the chance that someone will be willing to pay more than you did for an inherently worthless investment, because they think someone will pay more than they did, and so forth.

From Salon

She said the virus may in the end not end up becoming more virulent or efficient at moving between people, “but I don’t think we want to wait around and on the chance that it might.”

From Los Angeles Times

Another explanation for this whole saga is that Melania is simply trying to cash in on the chance that Trump loses and she has less cultural capital.

From Slate