Sprinkle brisket with salt and pepper; set aside 1 hour.
Soak mesquite chips in water to cover; set aside.
Prepare charcoal fire in grill, and let burn 45 minutes to 1 hour or until coals are white and moderately hot. Drain mesquite chips, and add 4 chips to charcoal, reserving remaining chips.
Place brisket on grill 8 inches from coals. Cover and cook over coals 4 to 5 hours or until desired degree of doneness. Turn brisket, and baste with Basting
Sauce every 20 minutes. Add charcoal and soaked chips to fire as necessary to maintain heat and smoke.
To serve, cut diagonally across the grain into thin slices.