Preheat your grill to medium-high heat.
Season the chicken breasts with salt and pepper.
Grill the chicken for 6-7 minutes on each side, or until cooked through.
While the chicken is grilling, cook the fettuccine according to package instructions.
In a saucepan, melt butter over medium heat, then add minced garlic and sauté until fragrant.
Add heavy cream to the pan, and cook on low heat for about 5 minutes.
Stir in the Parmesan cheese, mixing until melted and well combined.
Slice the grilled chicken into strips.
Combine cooked fettuccine with the Alfredo sauce, use reserved pasta water to adjust consistency as needed.
Gently fold in the sliced grilled chicken and season with additional salt and pepper to taste.
Serve hot, garnished with fresh parsley.