Reduce the balsamic vinegar to a syrup by simmering the vinegar in a saucepan over medium heat for about 10 minutes. When reduced to approximately 1/2 cup, transfer the balsamic syrup to a small cup and set aside.
Cut watermelon in inch thick triangles and cut the feta cheese in triangles as well. Assemble on a platter, either stacking or overlapping the watermelon and feta triangles. Sprinkle mint chiffonade on top and drizzle it with balsamic syrup.