For sauce, in a small saucepan, combine plum sauce, water, hoisin sauce, sesame seeds, ginger, chili sauce, and garlic.
Bring to boiling over medium heat, stirring frequently, and reduce heat. Simmer covered for 3 minutes. Remove saucepan from heat.
Grill chicken on the rack of an uncovered grill directly over medium coals for 12 to 15 minutes or until chicken is no longer pink (170°F for breast and 180°F for thighs). Turn once and brush with some sauce during the last 5 minutes of grilling. Serve with remaining sauce.