Season chicken with salt & pepper & dredge in flour. In a large skillet over Medium High heat, melt 2 T butter with 3 T olive oil. When they start to sizzle, add 2 pieces chicken & cook 3 min. When browned, flip over & cook other side for 3 min. Remove & transfer to a plate. Cook remaining chicken in same manner, and remove to a plate.
Into the pan, add the lemon juice, stock & capers. Return to stove & bring to boil, scraping up brown bits from pan. Return all chicken to the pan & simmer for 5 mins. Remove chicken to platter. Add remaining 2 T butter to sauce & whisk vigorously. Pour sauce over chicken & garnish with parsley.
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