Season chicken with salt and pepper. In a large pot, add 3 tablespoons of butter over medium-high heat. Add chicken and cook for 5 minutes stirring frequently. Add garlic; cook 30 to 60 seconds, stirring constantly, until fragrant.
Pour in chicken broth, lemon juice, zest, and uncooked penne. Bring liquid to a boil, then reduce heat to medium and simmer for 10 to 12 minutes. Stir occasionally until pasta is cooked, most of the liquid is absorbed, and it has a creamy, slightly thickened consistency. Remove from heat and immediately stir in the remaining 3 tablespoons of butter, cream, capers, and parsley.