Place chicken breasts between two pieces of plastic wrap and pound to an even 1/2-inch thickness. Season both sides with salt and pepper, then dredge in flour, shaking off excess.
Heat olive oil in a large skillet over medium-high heat. Add chicken and cook 4-5 minutes per side until golden brown and cooked through (internal temperature of 165°F). Transfer to a plate and tent with foil.
In the same skillet, melt 2 tablespoons butter over medium heat. Add garlic and cook for 30 seconds until fragrant.
Pour in chicken broth and lemon juice, scraping up any browned bits from the bottom of the pan. Simmer for 3-4 minutes until sauce reduces by half.
Remove from heat and stir in remaining 2 tablespoons butter until melted and sauce is glossy. Return chicken to the skillet, spoon sauce over top, and garnish with fresh parsley before serving.