Season all sides of the chicken with salt and pepper.
Add flour to a bowl to dredge the chicken in. Shake off excess flour.
Melt 2 tbsp butter along with 3 tbsp olive oil in a large skillet over medium high heat.
When the oils start to sizzle, add 2 pieces of chicken and cook for 5-8 minutes on each side (internal temp 165°F). Remove the chicken and place on a plate.
Leave juices and oil in the pan and add lemon juice, chicken stock and capers. Bring the mixture to a boil, scraping up any brown bits from the bottom of the pan to add flavor. Taste and season accordingly.
Return the chicken to the pan and simmer for 5 minutes. Remove chicken and place on a platter.
Add 2 more tbsp butter to the pan and whisk the sauce vigorously.
Pour the sauce over the chicken and garnish with parsley.