1In small bowl, mix mustard and soy sauce. Brush 3 tablespoons of mixture over chicken. Stir 6 tablespoons of the apricot preserves and the sesame seed into remaining mustard mixture; set aside.
2Heat gas or charcoal grill for indirect cooking. For two-burner gas grill, heat one burner to medium; place chicken on unheated side. For one-burner gas grill, place chicken on grill over low heat. For charcoal grill, move medium coals to edge of firebox; place chicken on grill rack over drip pan.
3Cover grill; cook 15 minutes. Turn chicken. Cover grill; cook 20 to 30 minutes longer, turning occasionally, until juice of chicken is clear when thickest piece is cut to bone (165°F).
4Brush chicken with reserved apricot mixture. Cook, turning and brushing frequently, 3 to 5 minutes, just until browned. Remove chicken from grill; spoon remaining 6 tablespoons apricot preserves over chicken.