Remove 1 chile from can, and mince. Place 1 teaspoon minced chile in a large zip-top plastic bag. Reserve 1/2 teaspoon minced chile, and set aside. Reserve the remaining chiles and sauce for another use. Add teriyaki sauce, chicken, and 2 teaspoons garlic to bag; seal and marinate in refrigerator 3 to 12 hours.
Heat oil in a medium nonstick skillet over medium heat. Add 1 teaspoon garlic and onion, and cook for 5 minutes or until tender, stirring frequently. Add the reserved 1/2 teaspoon minced chile, chopped apricots, preserves, lime juice, and 1/2 teaspoon salt; cook mixture over medium-high heat for 5 minutes or until apricots are very tender. Remove from heat; cool slightly. Place apricot mixture in a blender; process until smooth. Cool to room temperature. Remove 1/2 cup apricot mixture.
Remove the chicken from the bag, and discard the marinade. Sprinkle the chicken with 1/4 teaspoon salt. Place the chicken on grill rack coated with cooking spray, and grill for 10 minutes on each side, basting frequently with the reserved 1/2 cup apricot mixture during the last 5 minutes. Serve chicken with remaining apricot mixture. Sprinkle with cilantro.