Cook the fettuccine according to package instructions until al dente. Drain and set aside.
While the pasta is cooking, season the chicken breasts with salt and pepper on both sides.
In a large skillet, heat 2 tablespoons of olive oil over medium heat. Add the chicken and cook for about 6-7 minutes on each side, or until cooked through and golden brown. Once done, remove from the skillet and let it rest for a few minutes before slicing.
In the same skillet, add the remaining tablespoon of olive oil and minced garlic. Sauté for about 1-2 minutes until fragrant, being careful not to burn the garlic.
Pour in the heavy cream and bring to a simmer. Stir in the grated Parmesan cheese until melted and the sauce is smooth. If the sauce is too thick, you can add a little pasta water to reach your desired consistency.
Slice the cooked chicken and add it to the sauce along with the drained fettuccine. Toss everything together until the pasta and chicken are coated with the sauce.
Serve immediately, garnished with chopped parsley.
For added flavor, consider adding crushed red pepper flakes for a little heat.
This dish pairs well with a side salad or garlic bread. Enjoy!