on the chance that

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.
See also: chance, on
References in classic literature ?
Let him neglect the responsibilities of his office, and he will inevitably anchor himself on the chance that the thing left undone may turn out not to be of the supposed importance.
After leaving Magdalen, Frank had waited in the shrubbery, at a safe distance, on the chance that she might detach herself from her sister's company, and join him again.