Prepare the Marinade. Add all ingredients for the marinade (coconut milk, soy sauce, garlic, fresh ginger, and honey) in a medium bowl and mix until fully combined.
Marinate the Chicken. Transfer the chicken and marinade to a large ziplock bag and mix well to fully cover the chicken with the sauce. Allow the chicken to marinate in the refrigerator for at least 30 minutes to overnight.
Prepare the Peanut Sauce. whisk all ingredients for the peanut sauce together in a small saucepot over medium-low heat. Cook, stirring often, until smooth, warmed through, fully combined, and at your desired consistency. If your sauce is too thick, add water to thin until desired consistency is reached. Remove from heat and set aside.
Grill. When ready to cook, preheat an outdoor grill, indoor electric grill, or grill pan to medium heat. Oil the grates. Add the chicken and grill for approximately 6-8 minutes per side, or until internal temperature reaches 165 degrees F as read by a digital thermometer.
Serve. Remove chicken from the grill and drizzle with the warm Thai peanut sauce. Serve garnished with fresh basil, cilantro, and crushed peanuts, if desired.