In a saucepan, boil water, bring to a boil and salt it then cook the pasta according to the package instructions.
In a pan, over medium high heat, heat oil and add the chicken. Season with salt and pepper and cook the chicken for 4-5 minutes. If you have an instant read thermometer, the internal temperature of the chicken must register at 165°F (74°C).
Move the chicken to the sides of the pan, and melt the butter. Add the garlic and cook for 1 minute.
Add the cream and the lemon juice, and whisk or stir until you get a smooth sauce. Add the parmesan and stir until it's melted in the sauce.
If the sauce is too thick, add a little bit of pasta water to loosen it and whisk again.
Add the pasta, and mix everything together, the pasta with the sauce and the chicken. Taste the pasta with the sauce, and adjust seasonings to your preference.
Garnish with extra parmesan cheese, chopped parsley, and lemon zest.