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.

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.