Line a rimmed baking sheet with foil and set an oven rack on top. In a small bowl, mix brown sugar and ketchup. Set aside.
Wrap each whole water chestnut in a piece of bacon and secure with a toothpick. Dredge each in sauce mixture (or brush sauce on with a pastry brush).
Arrange in a single layer on rack set over baking sheet. Broil on HIGH 4 to 6 inches from broiler for 5 to 7 minutes per side (flipping halfway), about 10 to 15 minutes total. Remove from oven and serve warm.