Cut chicken livers into 24 (roughly 1/2-inch) pieces. Stir together soy sauce, ginger, brown sugar, and curry powder.
Add livers and water chestnuts and toss to coat. Marinate, covered and chilled, 1 hour.
While livers marinate, soak toothpicks in cold water 1 hour.
Drain well.
Preheat broiler.
Remove livers and chestnuts from marinade and discard marinade.
Place 1 piece of bacon on a work surface and put 1 piece of liver and 1 chestnut in center. Wrap bacon around liver and chestnut and secure with a toothpick. Make 23 more rumaki in same manner.
Broil rumaki on rack of a broiler pan 2 inches from heat, turning once, until bacon is crisp and livers are cooked but still slightly pink inside (unwrap 1 to check for doneness), 5 to 6 minutes.