Wash and dry the chicken breasts and trim off any fat. Cut the chicken into strips 4 inches long and 1/2 inch wide. Combine the ingredients for the marinade in a mixing bowl, add the chicken, and marinate for 20 minutes. Soak the skewers in cold water for 3 minutes to prevent them from burning.
Thread or impale the chicken strips on the skewers. (With the former, you'll wind up with a wavy look; with the latter you'll have straight satays.) Preheat a grill or broiler to high. Grill the satays until cooked, about 1 minute per side. You can protect the skewers with aluminum foil should they begin to burn.
Transfer the satays to plates or a platter and serve with tiny bowls of Peanut Sauce. Sprinkle the satays with chopped cilantro, if desired, and serve at once.