Preheat a gas grill to high or build a fire in a kettle grill.
Slice eggplant 1/3- to 1/2-inch thick. In a small bowl, mix together the olive oil, balsamic vinegar, garlic, salt and pepper. Brush both sides of the eggplant slices with the mixture.
Place eggplant on the preheated grill. If you wish to have nice grill lines, turn only once on each side. Grill eggplant slices 10 to 14 minutes.