Bring a large pot of salted water to a boil. Add the penne pasta and cook according to package instructions until al dente. Drain and set aside.
While the pasta cooks, heat the 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 for 5-7 minutes, stirring occasionally, until the chicken is cooked through and lightly browned. Remove the chicken from the skillet and set aside.
In the same skillet, add the minced garlic and sauté for about 1 minute until fragrant, stirring constantly to avoid burning.
Pour in the chicken broth, lemon juice, and add the lemon zest. Stir to combine and bring the mixture to a simmer.
Let the sauce simmer for 3-4 minutes to reduce slightly.
Reduce the heat to low and stir in the heavy cream and Parmesan cheese. Cook for another 2 minutes until the sauce is creamy and smooth.
Return the cooked chicken to the skillet and add the drained pasta. Toss everything together to coat the pasta and chicken evenly with the lemon sauce.
Remove from heat and stir in the chopped fresh parsley.
Serve the lemon chicken pasta hot, garnished with additional Parmesan cheese if desired.