Brush bread and sweet peppers with the 2 tablespoons olive oil. Place bread and sweet peppers on the rack of the grill directly over medium heat. Grill bread slices for 2 to 4 minutes or until browned, turning once halfway through grilling; set aside. Grill sweet peppers for 20 minutes, turning once halfway through grilling. Wrap sweet peppers in foil; let stand for 10 minutes.
Peel sweet peppers and cut into 1-inch pieces. In a large bowl toss together sweet pepper pieces, tomatoes, and cucumber.
In a small bowl combine the 1/4 cup olive oil, the red wine vinegar, salt, and black pepper. Drizzle half of the oil mixture over the vegetable mixture. Toss to coat. Let stand at room temperature for 30 minutes. Arrange bread slices on a serving platter. Top with vegetable mixture and chives. Pass remaining oil mixture. Makes 4 to 8 servings.