Season chicken with salt and pepper. Dredge chicken in flour, shaking off excess. Heat olive oil in 12" skillet over a high flame. Add chicken in a single layer. Cook until golden on bottom, about 2 minutes; turn. Cook on other side until golden, about 2 minutes. Remove to platter and cover with foil to keep warm. Add shallots and garlic to skillet, cook, stirring for 1 minute. Add chicken stock and reduced over high heat for 1 minute, scraping up any browned bits. Add balsamic vinegar and cook until sauce reduces and becomes syrupy (about 1 minute). Stir in basil, pour over chicken and serve.