"Chicken cacciatore is typical Tuscan dish, traditionally cooked in a terracotta pot with caramelized onions, capers, olives, tomatoes, and herbs. As a final touch, fried potatoes are added to the pot, too."
Bring a small pot of water to a boil. Add olives and celery; simmer until celery is bright green, about 30 seconds. Drain well.
Combine onions, water, and sugar in a saucepan over medium heat. Cover and cook, stirring occasionally, until onions are soft and caramelized, about 30 minutes.
Heat 1 tablespoon olive oil in a large skillet over medium heat. Cook chicken pieces until browned, about 4 minutes per side.
Transfer chicken pieces to a large saucepan; add olives, celery, caramelized onions, tomatoes, basil, lemon juice, capers, salt, and pepper. Cover and cook over medium heat until chicken is no longer pink in the center, about 1 hour.
Heat 1/4 cup olive oil in a deep skillet. Add potatoes; cook and stir until crisp and golden brown, about 10 minutes. Stir potatoes into the saucepan shortly before removing from the heat.