Bring a large pot of salted water to a boil. Cook fettuccine according to package instructions until al dente. Drain well and set aside.
Season the chicken breasts evenly with salt and black pepper.
Heat olive oil in a large skillet over medium-high heat. Add the chicken breasts and cook for 6-7 minutes per side, or until the internal temperature reaches 165°F. Remove from skillet, let rest for 5 minutes, then slice into strips.
In a separate large skillet or saucepan, melt the butter over medium heat. Add the minced garlic and sauté for 1 minute until fragrant.
Pour in the heavy whipping cream, stirring constantly, and bring to a gentle simmer. Let it cook for 2 minutes until it begins to slightly thicken.
Reduce the heat to low. Gradually whisk in the freshly grated Parmesan cheese until completely melted and the sauce is smooth. Season with salt and pepper to taste.
Add the cooked fettuccine to the sauce, tossing gently until the pasta is fully coated.
Top the creamy pasta with the sliced grilled chicken and garnish with freshly chopped parsley before serving.