In a gallon size ziplock bag, combine chicken thighs, coconut milk, and curry paste. Remove air from bag before sealing. Massage marinade into chicken until well-coated. Refrigerate for 6 to 8 hours. (If you don't have a ziplock bag, use a large mixing bowl and cover tightly with plastic wrap.)
Before cooking chicken, prepare Cilantro-Peanut Salad by combining cilantro, peanuts, sesame oil, sesame seeds, fresh lime juice, soy sauce or tamari, and chile (if using) in a bowl; mix well. Taste and add a pinch of salt, if needed. Set aside while you cook the chicken. (The cilantro will soften as it sits.)
Preheat grill, grill pan, or skillet over medium heat. Coat grill grates or pan with cooking oil. Remove chicken from marinade; discard marinade. Sprinkle chicken evenly with kosher salt. Arrange chicken on grill (or in pan), and cook for about 5 minutes per side, or until cooked through.*Note: If you prefer baking the chicken, place chicken thighs in a 9x13-inch baking dish and bake at 425ºF for 20 to 25 minutes, until it reaches an internal temperature of 165ºF.
Arrange chicken on a platter and scatter Cilantro-Peanut Salad overtop. Serve with lime wedges for squeezing over each serving.
