Heat gas or charcoal grill. In small saucepan, combine shallots, wine and 3 tablespoons lemon juice. Bring to a boil over medium-high heat. Reduce heat to medium; cook 5 to 7 minutes or until mixture is reduced to about 2 to 3 tablespoons, stirring occasionally.
Remove from heat. Stir in cold butter 1 tablespoon at a time until each is well blended. Stir in dill, chives and 1/8 teaspoon pepper. Cover to keep warm.
In small bowl, combine oil and 1 tablespoon lemon juice; mix well. Brush over salmon fillets. Sprinkle with salt and 1/4 teaspoon pepper.
When grill is heated, place salmon, skin side up, on gas grill over medium heat or on charcoal grill 4 to 6 inches from medium coals. Cook 8 to 10 minutes or until fish flakes easily with fork, turning once and brushing occasionally with any remaining oil mixture. If necessary, reheat butter sauce over very low heat, stirring constantly. Serve salmon with butter sauce.