In a large glass measuring cup, stir together the lemon juice, olive oil, rosemary, garlic, salt (and pepper if using). Set aside.
Pound the chicken breasts to an even thickness and cut into strips.
Place the chicken in a large bowl or casserole dish and pour marinade on top. Toss to coat well, cover & refrigerate 2-3 hours. (Don’t marinate longer than this. Lemon juice is a strong, fast-acting marinade).
Preheat a gas grill for 10 minutes on high. Then turn heat down to medium and grill the chicken, covered, for 4 minutes per side.