In a large bowl, coat eggplant with olive oil and balsamic vinegar. Season with salt and pepper.
Arrange half of the eggplant slices on a tray. Place a slice of tomato and a slice of goat cheese on each slice of eggplant. Sprinkle a little salt and pepper on the tomatoes and cheese. Top with remaining slices of eggplant, and secure each bundle with a toothpick.
Lightly oil the grill grate. Remove toothpicks, and arrange bundles on grate. Cook about 7 to 8 minutes, then carefully flip. Continue cooking for 6 to 7 minutes.
