Spread tomato evenly onto several layers of heavy-duty paper towels. Cover with additional paper towels; let stand 10 minutes.
Heat a large nonstick skillet over medium-high heat. Coat pan with cooking spray. Add eggplant and onion; sauté 10 minutes or until eggplant is tender and beginning to brown. Stir in thyme and pepper; cook 1 minute, stirring occasionally. Spoon eggplant mixture into a large bowl.
Coat pan with cooking spray. Add tomato; cook 2 minutes, stirring frequently. Stir tomato into eggplant mixture. Cool to room temperature.
Stir olives and next 5 ingredients (through vinegar) into eggplant mixture.
Cut French bread loaves in half horizontally. Hollow out top and bottom halves of bread, leaving a 1/2-inch-thick shell; reserve torn bread for another use. Spread about 3 tablespoons olive mixture over bottom half of each loaf. Arrange chicken evenly on bottom halves. Top chicken evenly with remaining 3 tablespoons olive mixture; cover with top halves of loaves. Wrap loaves with plastic wrap; refrigerate up to 24 hours. Cut each loaf into 3 pieces just before serving.