Stir together the Teriyaki sauce, preserves, ¼ cup cilantro leaves, lime juice, sesame oil, ginger, garlic, and jalapeno in a medium bowl. Reserve 1/3 cup mixture and store covered in the refrigerator.
Place chicken and remaining Sticky-Sweet Marinade in a large resealable bag and seal well; refrigerate for 2 hours (or up to 24 hours).
Allow reserved marinade to come to room temperature. If using wooden skewers, soak in water for 30 minutes.
Remove chicken from bag and discard bag and marinade. Thread chicken onto skewers. Cook on a well-oiled grill over medium-high heat for 3 to 4 minutes on each side or until chicken is cooked through. Transfer from grill to a platter and drizzle with reserved marinade. Garnish with cilantro and lime zest, if desired.