Boxer briefs are a good choice IMO, of some quick-drying hi-tech material. Then if you get chaffing that way (and you still might), swap to go commando for a day or more (great way to wash and dry your only pair of underwear too, and they add a real touch of "experienced hiker" panache drying on the back of your pack as you walk ... :-)).

As someone already mentioned, I think, walking yourself thinner might help the chaffing. Depends on the type of chaffing. But generally speaking, the "alternate boxer briefs and nothing" seems to work for me when a bit of chaffing is an issue.
Brian Lewis