In a small saucepan, melt butter over low heat. Stir in the mustard, vinegar, salt, pepper, garlic and hot pepper sauce. Cook and stir until heated through; remove from the heat.
Grill chicken, covered, over medium heat, turning occasionally, for 20 minutes. Brush with sauce. Continue basting and turning chicken several times for an additional 10 minutes or until a thermometer reads 180°.