Cook the pasta according to package instructions until al dente. Drain and set aside.
Season the chicken breasts with salt and pepper.
In a large skillet, heat olive oil over medium-high heat. Add the chicken and cook for 6-7 minutes on each side, or until cooked through and golden brown. Remove the chicken from the skillet and let it rest for a few minutes before slicing it into strips.
In the same skillet, add the minced garlic and sauté for about 30 seconds until fragrant.
Pour in the chicken broth and bring to a simmer, scraping up any browned bits from the bottom of the pan.
Stir in the heavy cream, Parmesan cheese, lemon juice, and lemon zest. Cook for 2-3 minutes, stirring until the sauce thickens slightly.
Add the cooked pasta and sliced chicken to the skillet, tossing to coat everything in the creamy sauce. Cook for an additional 2-3 minutes until heated through.
Garnish with chopped parsley before serving.