1. Lay a chicken breast on parchment paper. Starting on 1 long side, cut horizontally into breast but not completely through. Open cut breast like a book. Top with another sheet of parchment. Flatten to an even thickness, about 1/3 inch thick. Repeat with remaining breasts.

2. Rub both sides of each breast with garlic; transfer chicken and garlic to a large resealable plastic bag. Squeeze 2 lemon halves over chicken; add rinds to bag. Thinly slice remaining lemon halves crosswise. Top each breast with a lemon slice and thyme sprig; season with pepper. Drizzle chicken with oil. Marinate in the refrigerator, flipping occasionally, at least 2 hours (up to overnight).

3. Preheat a grill or grill pan to high. Discard marinade, lemon, and thyme. Season chicken with salt and pepper. Grill, flipping once, until cooked through, 2 minutes per side. Serve chicken warm, at room temperature, or cold. Top each breast with salad, dividing evenly, and serve with lemon wedges.