Preheat the oven to 350 degrees F. Line a large rimmed baking sheet with parchment paper. Lay the chicken breasts flat on the baking sheet. Starting from one side, cut a deep slit (or pocket) into each chicken breast, parallel to the baking sheet, leaving three sides intact. Try to make the cut even so the attached edges are all about 1/2-inch thick.
Chop the salami and olives. Shred the cheeses.
Into a mixing bowl, measure both kinds of cheese, diced salami, chopped olives, and capers. Mix well.
Stuff the mixture evenly into the chicken breasts, turning them upright, so the stuffing is facing up. Sprinkle the tops with ground black pepper.
Bake for 25 minutes, until the chicken breasts have cooked through and the filling is bubbly. Serve warm.