Bring a large pot of salted water to a boil and cook fettuccine according to package directions until al dente.
Season chicken breasts with salt and pepper on both sides.
Heat olive oil in a large skillet over medium-high heat and cook chicken for 6 to 8 minutes per side until the internal temperature reaches 165°F (74°C).
Remove chicken from the skillet and let it rest for 5 minutes before slicing into strips.
In a medium saucepan or the same skillet over medium heat, melt the butter.
Add minced garlic and sauté for 1 minute until fragrant but not browned.
Whisk in the heavy cream and bring to a gentle simmer.
Gradually stir in the grated Parmesan cheese until completely melted and the sauce has thickened slightly.
Stir in the ground nutmeg and adjust seasoning with salt and pepper as needed.
Toss the cooked fettuccine with the Alfredo sauce until the pasta is thoroughly coated.
Divide the pasta into bowls, top with sliced chicken, and garnish with chopped parsley.