Combine half of each of the tomato, cucumber, onion, and green pepper in a large bowl. Add 1/2 cup tomato juice; mix well. Puree vegetable mixture in blender.
Place remaining half of vegetables in separate serving bowls; cover and refrigerate.
Combine pureed vegetables, remaining tomato juice, 1/3 cup olive oil, vinegar, hot sauce, salt, and pepper in a large bowl, mixing well. Cover, and refrigerate at least 3 hours.
Rub inside of small skillet with halved garlic cloves; reserve garlic. Place 2 tablespoons olive oil in skillet, and sauté bread cubes over medium heat until golden brown. Drain well; place in a small serving dish.
To serve, mince reserved garlic; stir into chilled soup mixture, and sprinkle with chives. On a tray, arrange chopped vegetables and croutons to be sprinkled over the top of each serving.