Set a rack in the upper third of the oven. Line the bottom of a broiler pan with foil, replace the perforated top part of the pan, and put the whole pan on the oven rack. Heat the oven to 450°F.
In a medium bowl, combine the soy sauce, brown sugar, and ginger. If the muscle tabs from the sides of the scallops are still attached, peel them off and discard them. Cut each scallop into quarters. Marinate the scallop pieces in the soy mixture for 15 minutes. Reserve the marinade.
To assemble, stack 2 slices of water chestnut in the center of a piece of the bacon. Put a piece of scallop on top of the water chestnuts. Wrap each end of the bacon over the scallop and secure with a toothpick. Repeat with the remaining bacon, water chestnuts, and scallops (you may not use all of the water chestnuts).
Remove the broiler pan from the oven and quickly arrange the bacon-wrapped scallops on the hot pan so that an exposed side of each scallop faces up. Drizzle the scallops with the reserved marinade. Bake, turning the scallops over once after 10 minutes, until the bacon is browned around the edges and the scallops are cooked through, about 15 minutes total.