Season chicken with salt and pepper. Heat 1 tablespoon oil in a large nonstick skillet over medium-high. Add half of chicken and cook, flipping once, until browned and cooked through, about 6 minutes total; transfer to a plate. Repeat with remaining chicken and 1 more tablespoon oil.
Step 2
Reduce heat to medium; add 1 tablespoon oil to skillet, then bread and juices from chicken plate. Cook, stirring, until golden, 5 minutes. Let cool slightly. Transfer to a bowl with tomatoes, capers, celery hearts and leaves, vinegar, and 1 tablespoon oil. Season with salt and pepper. Fold in cheese and basil; serve with sliced chicken.