Rinse the chicken breasts and pat dry with paper towels. 2 In a small bowl, combine the garlic, rosemary, sherry, 1 tbsp salt, and 3/4 teaspoon pepper. Stir to form a paste.
Find the spot where the breast meat meets the rib bones. Slide your finger between the two, and stuff as much paste into each chicken breast as possible.
Place the stuffed breasts in a big bowl. Pour in the olive oil and turn to coat. Let stand for 15 minutes.
Prepare an indirect-heat fire in a covered charcoal grill.
Place the chicken breasts, skin side down, on the grill rack and grill, uncovered, for 4 minutes. Cover, open the top and bottom vents fully, and grill for 6 minutes longer. Uncover, turn the chicken, sprinkle with salt and pepper, re-cover, and grill until cooked through, another 10 minutes, for a total of 20 minutes.
Remove to a platter and serve hot.