I think both can be grammatically correct. (If we could read the full sentence, we might have a strong preference for #2 or #1...or we might think that both options sound fine for that sentence).
#2 is definitely more common. When I typed the full phrases with quotation marks into a Google search, "There is no chance that" had 2,570,000 results. "There are no chances that" had just 57,000 results (but some of these were in published books, The New York Times, etc., so that suggests that they may not all be grammar mistakes that were typed on the Internet by people who don't use good grammar).
So, I don't think we can say that #1 is always wrong or always sounds worse. I can create a sentence that I think sounds fine with #1: "There are no chances that are worth taking in situations where you fear that any of those chances could cause death."