In a medium bowl, stir together the coconut milk, ground coriander, curry powder, fish sauce, and chili oil. Add the chicken breast strips, and stir to coat. Cover, and refrigerate for at least 30 minutes, and up to 2 hours.
Preheat an indoor or outdoor grill for high heat. Thread the chicken strips onto skewers. Discard marinade.
Grill chicken for 2 to 3 minutes per side, until no longer pink. Time will depend on how thick your strips are. Transfer to a serving plate, and garnish with cilantro and peanuts. Serve with peanut sauce for dipping.