Chamfering internal corner with round edge?

I need to apply a chamfered edge to an interior corner- basically, the path you get with a V-groove bit traveling a rectangular path.

Chamfering the corner gives me a sharp edge at that corner. Is there a way to make the corners blend instead of just having each chamfer go straight into each other? I basically need the "Round corners" checkbox available in the Fillet menu but for chamfers.