I assume that you've already made the chilli. (if not, I'd suggest using less chilli but adding ground cayenne to retain the flavour).
Somewhat surprisingly, black pepper seems to take the heat out of a chilli. Alternatively, why not leave the chilli as it is, but serve it with sour cream to act as a 'cooling agent'?
Agree with Bednobs, sugar will help. If you don't want to add any milk product, you could make up more, leave out the hot stuff, then mix the two lots together. Freeze the extra. It freezes well.