Slice a 2-inch deep slit into the side of each chicken breast, taking care not to cut all the way through.
Place 3 mozzarella cubes inside each slit.
Add 2 teaspoons pesto to each slit and close each breast using a toothpick.
Season all over with salt and pepper.
Grill the chicken, flipping once, until cooked through to an internal temperature of 165°F, 10 to 12 minutes per side. Let the chicken rest for a few minutes before slicing and serving.
Notes
Checking for doneness--When checking the internal temperature of the chicken, poke it in a few places to make sure you're measuring the meat and not the cheese or pesto.
Dietary--This recipe is suitable for gluten-free diets.