Bring a large pot of salted water to a boil. Add the penne pasta and cook according to package instructions until al dente, about 10-12 minutes. Drain and set aside.
While the pasta cooks, heat olive oil in a large skillet over medium-high heat.
Season the chicken pieces with salt and black pepper.
Add the chicken to the skillet and cook, stirring occasionally, until golden brown and cooked through, about 6-8 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the minced garlic and sauté for 1 minute until fragrant.
Pour in the chicken broth, lemon juice, and add the lemon zest. Bring the mixture to a simmer and cook for 3-4 minutes to reduce slightly.
Reduce the heat to low and stir in the heavy cream, Parmesan cheese, and butter. Stir until the cheese and butter have melted and the sauce is smooth.
Return the cooked chicken to the skillet and toss to coat in the sauce.
Add the drained pasta to the skillet and gently toss everything together until the pasta is well coated with the lemon chicken sauce.
Sprinkle the chopped fresh parsley over the top and serve immediately.