Start by marinating the chicken breasts with olive oil, salt, and pepper. Let them sit for at least 30 minutes to absorb the flavors.

Preheat your grill or grill pan over medium-high heat. Grill the chicken for about 6-7 minutes on each side, or until fully cooked and the internal temperature reaches 165°F (75°C). Once done, remove from the grill and let it rest for 5 minutes before slicing into strips.

While the chicken is grilling, bring a large pot of salted water to a boil. Add the fettuccine and cook according to package instructions until al dente, usually about 10-12 minutes. Drain the pasta, reserving about 1 cup of the pasta water.

In a large skillet over medium heat, melt the butter. Add the minced garlic and sauté for about 1 minute until fragrant but not browned.

Pour in the heavy cream and bring to a gentle simmer. Reduce the heat to low and stir in the grated Parmesan cheese until melted and the sauce is smooth. If desired, add nutmeg for an extra layer of flavor.

Add the cooked fettuccine to the skillet, tossing it in the Alfredo sauce until well coated. If the sauce is too thick, gradually add a little reserved pasta water until you reach your desired consistency.

Toss in the sliced grilled chicken, mixing gently to combine everything. Season with additional salt and pepper to taste.

Serve immediately, garnishing with fresh parsley if desired.