Brush chicken with 1 tablespoon of the oil; sprinkle 1/4 teaspoon each salt and black pepper. On charcoal grill, cook chicken on rack directly over medium coals for 12 to 15 minutes or until no longer pink, turning once halfway through grilling time.
Place beans in microwave-safe 1-1/2-quart dish. Add 1 tablespoon water. Cover with vented plastic wrap. Cook on high 3 minutes; drain.
For Chimichurri sauce, in small food processor bowl combine parsley, the remaining oil, the vinegar, garlic, 1/4 teaspoon salt, and red pepper. Process until nearly smooth. Serve chicken and beans topped with Chimichurri sauce, lemon peel, and juice. Makes 4 servings.