Stir together tomatoes, olives, red onion, anchovy, vinegar, chili pepper, and garlic in a medium mixing bowl. Let stand at room temperature for 20 to 30 minutes.
Meanwhile, slice bread into 1/2-inch thick slices. Place bread slices on a baking sheet. Bake in a 350°F oven about 5 minutes or until brown. Turn bread over and bake 5 minutes more.
Arrange mozzarella cheese slices evenly on toasted bread.
Drain tomato mixture. Top each cheese slice with a spoonful of tomato mixture. Return bread slices to oven; bake for 5 minutes more or till cheese melts and tomato mixture is heated through.