It's more often singular chance rather than chances, but by far the most common preposition is of winning - with what I assume is a "continuous participle" verb form (but maybe it's a "gerund", I've never found that distinction particularly clear or useful myself).
The next most common form is to win, which I assume is a preposition use, followed by an "unmarked infinitive" verb form. The preposition at comes in a distant third in this NGram usage chart...
If you follow my link to that chart, you can toggle between AmE and BrE corpuses for more detail, but I don't think there's any significant difference between them. Feasibly Amnericans are slightly less likely than Brits to use the plural chances, but learners should probably just stick with the singular anyway, since it's far more common everywhere.
The main point to note is that the preposition is essentially a stylistic choice, primarily affected by the (again, stylistic) choice of verb form. That choice doesn't reflect any difference in meaning.