Season chicken breasts with salt and pepper on both sides.
In a large skillet, melt butter over medium heat. Add the chicken and cook for 6–7 minutes per side, or until golden and cooked through. Remove from the skillet and set aside.
In the same skillet, add garlic and sauté for 30 seconds until fragrant. Pour in the chicken broth and lemon juice, scraping up any browned bits.
Add lemon zest and fresh parsley, simmer for 2–3 minutes until slightly reduced.
Meanwhile, cook linguine according to package directions until al dente. Drain and add to the skillet.
Slice the cooked chicken and return it to the skillet.
Stir gently to coat everything in the sauce. Serve warm with extra lemon wedges and Parmesan if desired.