Cut eggplant into 1/2-inch (1 cm) thick slices; sprinkle with salt. Let stand in colander until moisture seeps out, about 10 minutes. Pat dry with paper towel.
Whisk together olive oil, balsamic vinegar, oregano, salt and pepper. Brush half over eggplant. Place on greased grill over medium heat; close lid and grill, turning once and brushing with remaining oil mixture, until tender, about 10 minutes.