Heat oil in a 12-inch heavy skillet over moderate heat until hot but not smoking, then fry capers, stirring, until slightly crisp and a shade darker, about 2 minutes. Transfer capers with a slotted spoon to paper towels to drain.
Pat chicken dry and season well with salt and black pepper. Heat oil remaining in skillet over moderately high heat until hot but not smoking, then sauté chicken in batches, turning once, until golden brown, 1 to 1 1/2 minutes per side. Transfer to a platter and keep warm, covered.
Remove skillet from heat. Add parsley and lemon juice to skillet and simmer over moderately high heat, stirring and scraping up any brown bits from bottom of skillet, 1 minute. Pour sauce over chicken and top with fried capers.