Cook pasta in salted boiling water until al dente. Reserve 1 cup pasta water, then drain.
Heat olive oil in a skillet over medium-high heat. Season chicken with salt and pepper, then cook 5–6 minutes until golden and cooked through. Remove and set aside.
In the same skillet, add garlic; sauté 1 minute until fragrant. Stir in lemon juice, lemon zest, and chicken broth. Simmer 2–3 minutes.
Add butter and parmesan, stirring until melted into a light sauce.
Return chicken and pasta to the skillet. Toss everything together, adding reserved pasta water as needed for creaminess.
Garnish with parsley and extra parmesan. Serve immediately.