Season both sides of chicken breasts with salt and pepper.
Place flour in a shallow dish. Dredge both sides of the chicken breasts in the flour, one at a time.
Heat a 12-inch skillet over medium-high heat.
Add olive oil and 1 Tbsp of butter. Let the butter melt, then add the chicken breasts in a single layer.
Sear until golden brown on the bottom, about 4 - 5 minutes, then flip and continue to cook until the chicken registers 165°F in the center, about 4 - 5 minutes longer.
Transfer the chicken to a plate while leaving any excess oil in the pan.
Reduce heat to medium. Add garlic and sauté for 20 seconds, or until just lightly golden brown.
Pour in the chicken broth while scraping up browned bits from the pan.
Pour in the lemon juice, bring the mixture to a simmer, and let it reduce by about half, about 2 minutes.
Add the remaining 3 Tbsp of butter and the lemon zest, stirring until the butter melts.
Return the chicken to the skillet, spoon the sauce over the chicken, and garnish with parsley. Serve warm.