Toss the diced bread with 1 tablespoon olive oil. Sprinkle with a pinch of salt and pepper and place on a sheet pan. Toast in the oven until golden, but still a little chewy, about 5 minutes.
Meanwhile, heat 2 tablespoons olive oil in a skillet over a medium-high heat. Sprinkle the chicken cutlets with salt and pepper and, when the oil is hot, add to the skillet. Fry, flipping as needed, until cooked through and nicely seared, 3 to 4 minutes per side.
Combine the tomatoes, garlic, basil chiffonade, the remaining 2 tablespoons olive oil, some salt and pepper and 1 tablespoon balsamic reduction in a bowl. Toss and set aside.
Remove the bread from the oven and, at the last minute, toss with the tomato mixture. Top the cooked chicken with the bread/tomato mixture, allowing it to fall around the edges and fill in the gaps of the skillet. Drizzle over the remaining 2 tablespoons balsamic reduction and garnish with some fresh basil leaves. Serve immediately.