Mix soy sauce, water, brown sugar, onions, garlic, sesame oil, and coconut milk in a large bowl. Place chicken breasts in marinade. Let chicken for at least 4 hours or overnight.
Grill chicken on a low heat so that the marinade does not burn for 5-7 minutes per side or until done. If you do not have a grill you can use a indoor grill pan.
Serve over rice, garnish with green onions and top with a little extra soy sauce.