Butterfly the chicken breasts to make them thinner, then cut them in half length ways to make long thin portions.
Preheat a large skillet or fry pan over medium high heat.
Season the chicken with the salt and pepper.
Dredge the chicken in flour and shake off the excess.
In the heated skillet add 2 Tbsp of oil and then melt 2 tablespoons of butter
When the butter and oil start to sizzle, add half of the chicken and cook for 3 minutes. When the chicken is browned, flip and cook other side for 3 minutes. Remove and transfer to a plate. Add another 2 tbsp butter and 2 tbsp of olive oil and repeat with the other chicken pieces, transferring to the plate when done.
Brown the garlic in the oil and butter, and then add the lemon juice, chicken stock and olives or capers to the pan. Bring to boil and deglaze the brown bits from the pan for extra flavor. Check the sauce for salt and pepper.
Return all the chicken to the pan and simmer for 5 minutes. Remove the chicken to a platter.
Add the remaining 2 tablespoons butter to the sauce in the pan and whisk vigorously. Pour the sauce over the chicken and garnish with parsley and lemon slices.
