Season chicken with salt and pepper. Dredge chicken in flour and shake off excess.
In large skillet over medium-high heat melt butter, melt 2 tbsp of butter with 3 tbsp of olive oil. When butter and oil starts to sizzle, add 2 pieces of chicken and cook for 3 minutes.
When chicken is browned, flip and cook the other side for 3 minutes.
Remove and transfer to plate. Melt 2 more tbsp butter and another 2 tbsp olive oil. When butter and oil start to sizzle, add the other 2 pieces of chicken and brown both sides in same manner.
Remove pan from heat and add chicken to the plate. Into the pan add the lemon juice, lemon zest, stock, white wine and capers. Return to stove and bring to boil, scraping up brown bits from the pan for flavor. Check for seasoning. Return all of the chicken to the pan and simmer for 5 minutes.
Remove chicken to the platter. Add remaining 2 tbsp butter to the sauce and whisk vigorously. Pour sauce over chicken and garnish with parsley.