I really don't like using scrapers, it seems much harder than using a
bowl gouge - Soren Berger makes a special tool for hollowing boxes, but
for one box/cup, try a 1/2 inch bowl gouge with very swept back wings -
once you get a basic shape inside, hollow "backwards" (from bottom to
top, with the handle of the tool on the far side of the lathe) with a
light cut - you shouldn't get chips - it is something about your tool
presentation or sharpness, particularly if you get catches. You can use
the gouge for the outside too - keep it really sharp