Thaw fish, if frozen. Rinse fish; pat dry with paper towels. Place fish in a resealable plastic bag set in a shallow dish. For marinade, in a small bowl combine parsley, chicken broth, lemon peel, lemon juice, rosemary, oil, shallot, tarragon, salt, and garlic. Pour marinade over fish; seal bag. Marinate at room temperature for 30 minutes, turning bag occasionally.
Drain fish, reserving marinade. Grill fish on the greased rack of an uncovered grill directly over medium coals for 5 minutes, brushing once with marinade. Turn fish and grill 3 to 7 minutes more or until fish flakes easily when tested with a fork. Discard any remaining marinade. Makes 4 to 6 servings.