Preheat a gas or charcoal grill for direct high-heat cooking, approximately 450°F to 500°F. Clean the cooking grates and lightly oil them.
Place each chicken breast flat on a cutting board. Carefully slice horizontally through the center to create 8 thin chicken cutlets.
If needed, place the cutlets between parchment paper or plastic wrap and gently pound the thicker areas until each piece is approximately 1/4 to 1/2 inch thick.
Whisk the garlic, rosemary, lemon juice, olive oil, kosher salt, and black pepper together in a mixing bowl.
Immediately transfer half of the lemon-herb mixture to a separate clean bowl. Reserve this clean portion for finishing the cooked chicken.
Add the chicken cutlets to the remaining mixture and turn until every piece is lightly and evenly coated.
Place the chicken directly over the hottest section of the grill.
Close the lid and cook primarily on the first side for 3 to 4 minutes. Rotate the pieces if needed for even browning, but do not flip yet.
When the chicken is nearly cooked through and only slightly underdone on top, flip each cutlet.
Cook for another 30 to 60 seconds, or until the thickest part of every cutlet reaches an internal temperature of 165°F.
Transfer the chicken to a clean platter and rest for approximately 2 minutes.
Whisk the reserved clean lemon-herb mixture again, then spoon it lightly over the grilled chicken.
Serve immediately with fresh lemon wedges if desired.