Preheat the grill to medium-high; lightly coat the grate with cooking oil. Remove the chicken from the marinade; discard the used marinade. Cook the chicken and the red pepper, turning and basting with the reserved soy mixture, for 15 to 20 minutes or until cooked through. Cool slightly.
TIP: Since the basting marinade already contains oil, skip greasing the grill; too much oil causes flare-ups.