Lightly brush both sides of chicken breasts with oil. For a charcoal grill, grill chicken on the rack of an uncovered grill directly over medium coals for 12 to 15 minutes or till chicken is tender and no longer pink (170 degrees F), turning once. (For a gas grill, preheat grill. Reduce heat to medium. Place chicken on grill rack over heat. Cover and grill as above.) Remove chicken from grill; immediately place in a shallow bowl or pie plate. Drizzle teriyaki sauce over chicken, turning to coat both sides. Let stand, covered, for 20 minutes, turning 2 or 3 times. Remove chicken from teriyaki, discarding teriyaki. Cut chicken into bite-size strips. Set aside.