Season the chicken breasts with salt and pepper.
Add the olive oil to a large skillet set over medium heat. Once the oil is hot, add the chicken breasts and cook, undisturbed, until they release naturally from the pan, about 5 minutes. Flip the chicken once and continue cooking until they are cooked through and reach an internal temperature of 165°F. (The remaining cook time will vary on the thickness of the breasts, but roughly an additional 3 to 5 minutes.)
Transfer the chicken breasts to a plate and leave all dripping in the skillet.
Reduce the heat to medium-low then add the garlic and cook, stirring, until golden brown and fragrant, about 2 minutes.
Add the chicken stock and cook, scraping up any brown bits from the bottom of the skillet, for an additional 2 minutes until reduced slightly.
Whisk in the butter then once it has melted, whisk in the flour and cook until the sauce thickens slightly, about 2 minutes.
Remove the sauce from the heat and stir in the lemon juice and parsley. Taste and season the sauce with salt and pepper.
Spoon the garlic butter sauce over the chicken and serve.