Bring a large pot of salted water to a boil and cook the pasta until al dente.
Reserve 1/2 cup of the starchy pasta water, then drain the noodles.
Heat olive oil in a large skillet over medium-high heat.
Add the sliced chicken breasts to the skillet, seasoning with salt and pepper, and cook until golden brown and cooked through.
Stir in the minced garlic and cook for about 1 minute until fragrant.
Reduce heat to low and pour in the heavy cream and fresh lemon juice.
Add the cooked pasta and the reserved pasta water to the skillet.
Sprinkle in the parmesan cheese and lemon zest while tossing everything together to emulsify into a silky sauce.
Remove from heat once the sauce coats the noodles evenly.
Garnish with fresh parsley and serve immediately.