Spiralize the zucchini into thin noodles. Microwave the noodles for 2 minutes, drain the liquid.
In a large skillet, over medium heat, melt the butter. Sauté chicken, stirring frequently. Season with salt and pepper and add garlic. Cook until the chicken is cooked through and the garlic begins to brown.
Add heavy cream, Parmesan cheese and parsley; stir to combine. Bring to a boil, continue to stir until the sauce has reduced by about half. Remove from heat.
Toss in zucchini noodles; toss until noodles are evenly coated. Garnish with additional Parmesan cheese.