In a mixing bowl, combine coconut milk, soy sauce, brown sugar, curry powder, garlic powder, ginger, lime juice, salt, and pepper. Mix well to create the marinade.
Add the chicken cubes to the marinade, ensuring they are well coated. Cover and refrigerate for at least 30 minutes (or up to 2 hours for more flavor).
While the chicken is marinating, prepare the peanut sauce. In a blender or food processor, combine peanut butter, coconut milk, soy sauce, brown sugar, lime juice, red curry paste, and water. Blend until smooth. Adjust the consistency by adding more water if needed. Set aside.
Preheat the grill or grilling pan over medium-high heat. Thread the marinated chicken onto skewers.
Grill the chicken skewers for about 5-7 minutes on each side or until fully cooked and slightly charred.
Serve the grilled chicken satay with the peanut sauce on the side for dipping.