Heat 2 cups olive oil in a skillet over medium heat. Place the eggs and bread crumbs in 2 separate bowls. Dip chicken in the eggs then in the bread crumbs to coat. Place chicken in the skillet, and fry until golden brown and juices run clear. Drain on paper towels.
In a bowl, mix the tomatoes, onion, and basil. Season with salt and pepper, and drizzle with balsamic vinegar and olive oil. Spoon over the fried chicken to serve.
