Place cubed chicken a large zip-top bag. In a medium bowl, whisk together coconut milk, soy sauce, garlic, brown sugar, curry powder, ginger, salt and pepper.
Pour over chicken and seal bag. Refrigerate for at least an hour, or up to 8 hours.
Preheat grill for medium-high heat. Thread chicken onto skewers (discard marinade). Cook for about 10 minutes, or until chicken is no longer pink, turning once halfway through cooking time.