If you mean dried older woodchips, no particular problem that I know of as long as you understand they will not be absorbant and may be a bit harder to work with than some other beddings.
If you mean chippings from having run a tree thru a chipper yesterday or last week, that can be more of a problem because fresh chippings are QUITE prone to heating up and molding, two things you definitely don't want. If you can leave them outside to dry in a thinnish layer for at least a few weeks, then you might consider using them, although again remember they will not be absorbant and may still cause more of a moisture problem that you might wish in some circumstances. You'd want to keep a close eye on things. And it will depend a lot on your situation and climate.