Cook the fettuccine pasta according to package instructions until al dente.
While the pasta cooks, melt the butter in a large skillet over medium heat.
Add minced garlic to the skillet and sauté for about 30 seconds until fragrant.
Pour in the heavy cream, stirring constantly to combine, and bring to a gentle simmer.
Gradually whisk in the grated Parmesan cheese until melted and the sauce is smooth.
Season with salt and pepper to taste before adding the shredded chicken to the sauce.
Drain the cooked pasta and add it directly to the sauce, tossing to coat well.
Let the pasta sit for a minute to absorb more sauce, then plate and garnish with parsley.