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 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.
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