Prepare the grill to medium-high heat.
Slice the tomato, slice the mozzarella, and chop the basil.
Grill the chicken, uncovered, for 5 to 8 minutes on each side, depending on the thickness. Test the chicken with a meat thermometer for an internal temperature of 165º.
Move the chicken to a platter and top each piece with a slice of fresh mozzarella. Using aluminum foil, tent the platter allowing the cheese to melt.
While the cheese is melting, place the remaining balsamic vinegar in a small saucepan with the brown sugar.
Bring mixture to a boil over medium high heat. As soon the vinegar mixture boils, immediately reduce the temperature to medium-low and reduce by half. The sauce will thicken as it cools.
If the sauce becomes too thick to spoon over the chicken, add a little water (2 teaspoons or so) and return to the heat. Stir until the mixture begins to thicken again. It won't take long.
To serve the grilled bruschetta chicken, remove the tented foil and top the cheese with a slice of fresh tomato.
Sprinkle with fresh basil and drizzle with the balsamic reduction. Enjoy while warm, though the leftovers are delicious cold, too!
Tip: You should give your grill a light cleaning after every use. Leaving it for later just makes it more difficult! After the grates cool, take a bristle-free grill brush and scrape away any food particles.