How do I add a chamfer to the inner square on the attached pic?

Quick and easy:

  1. Select the edges of the opening.
  2. Get the Offset tool and create offset lines outside those edges to the width of the chamfer.
  3. With the inside edges selected, get the Move tool. Hold Alt on the PC or Command on Mac to invoke Autofold and move the selection toward the back of the frame to the desired depth.

If you want a 45° chamfer, move the inside edges the same distance as the offset.

Just to give you an idea of how many ways there are to skin this cat, here are three more methods:

-Gully

Thanks DaveR and Gully_Foyle that was very helpful.