In a medium bowl, combine coconut milk, soy sauce, peanut butter, curry powder, turmeric, garlic, ginger, brown sugar, fish sauce, sesame oil and kosher salt.
In a gallon size Ziploc bag or large bowl, combine chicken and ¾ of the coconut milk mixture; marinate for at least 2 hours to overnight, turning the bag occasionally. Set the remainder of the milk mixture aside and refrigerate to brush on the meat while it’s on the grill.
Drain the chicken from the marinade, discarding the marinade that the chicken has been soaking in.
Preheat the grill to medium high heat. If you are using bamboo skewers, soak them in water for 10 minutes before adding the chicken. This will help keep them from burning on the grill. Thread chicken onto skewers. Brush with oil; Give each skewer a generous sprinkle of salt and pepper on each side.
Add skewers to grill, and cook, turning occasionally, painting with the marinade until the chicken is completely cooked through, reaching an internal temperature of 165 degrees F, about 12-15 minutes. Taste and check for salt and pepper level. Add more as needed.