In a large saucepan combine the eggplant, tomatoes, onion, peppers, wine, basil, garlic and 1/3 teaspoon salt. Bring to a boil, reduce heat. Simmer, cover for 10 minutes. Uncover and simmer 5 minutes more or until vegetables are tender and nearly all of the liquid is evaporated.
Meanwhile, rinse chicken; pat dry. Place each breast half between 2 pieces of plastic wrap. Working from the center to the edges, pound chicken lightly with the flat side of a meat mallet to 1/4 inch thickness. Remove plastic wrap and lightly salt chicken.
In a large frying pan heat the oil and paprika over medium-high heat. Add chicken and cook for 4 to 6 minutes or until tender and no pink remains, turning once.