Cut chicken livers, water chestnuts, and bacon in half. Place a chicken liver half and a water chestnut half on each half of bacon. Roll up and secure with a wooden pick, making sure pick goes through water chestnut. Place in a shallow baking dish.
Combine remaining ingredients; stir until sugar dissolves. Pour marinade over prepared rumaki; let stand at room temperature 1 hour, turning twice. Drain well on paper towels.
Place rumaki on a rack in a broiler pan. Broil until bacon is crisp, turning frequently to brown all sides.