Can you tell if the problem is with the mask, the strap, or the positions he sleeps in?
I use a nasal mask w/ chin strap, but I put the strap on with my jaw closed (but not clenched) and I sleep only on my back with a 12" foam wedge.
There are (at least) 2 basic ways of wearing the chin strap. One is around the point of the chin (like a helmet) and the crown of the head. The other is under the chin and around the top of the head.
There are many many kinds/designs/styles of masks (and cushions), and AFAIK there's no law that you have to be stuck with only what your supplier carries, so you/he can look/shop around. Most reputable suppliers will allow you to "test-drive" at home.
He might need/try a different style of mask, cushion (or both) or learn to sleep in positions that don't cause the problem (I hate it too).
google: cpap masks
google: cpap cushions
and click on Images in the lefthand column for some other options.
Dr. Zachary Smith
Oh, the pain... THE PAIN...
Dr. Smith is NOT a medical doctor. He was a character from LOST IN SPACE.
All opinions expressed are my own. For medical advice/opinion, consult your doctor.