Heat grill to medium. In a small saucepan, bring 1/3 cup water and rosemary to a boil; remove from heat, cover, and let steep 5 minutes. Transfer to a blender. Add oil and garlic; season with salt and pepper. Puree until smooth; let cool.
Combine chicken and rosemary oil in a shallow dish or resealable plastic bag, and turn to coat. Cover, and let marinate at least 15 minutes at room temperature or overnight in the refrigerator, turning chicken occasionally.
Remove chicken from marinade; place on grill. Discard marinade. Cook, basting frequently with lemon juice and turning as needed to prevent burning, until cooked throughout, 20 to 30 minutes. Serve with Grilled Zucchini and Squash.