Season chicken with salt and pepper on both sides.
Place flour in a shallow dish and then dredge both sides of the chicken breasts in flour, one at a time.
Heat a 12-inch skillet over medium-high heat.
Add the olive oil and 1 tablespoon of butter, melt the butter, and add the chicken breasts in a single layer.
Sear for around 5 min until the bottom is golden brown, then flip and continue cooking until the chicken in the middle is 165 degrees, about 4-5 minutes longer.
Place the chicken on a plate and leave it in a pan with a bit of excess oil.
Reduce to medium heat, add garlic and sauté for 20 seconds or until lightly golden brown, then pour in the broth of the chicken.
Pour the lemon juice, simmer the mixture, reduce the heat slightly, and simmer for about half, about 2 minutes until the liquid is reduced.
Add butter and lemon zest to the remaining 3 tablespoons and stir until the butter melts.
Put the chicken back into the skillet, cover the chicken with a spoonful of sauce and add the parsley to the garnish. Just serve it hot.