Bring a large pot of salted water to a boil. Add the fettuccine pasta and cook according to package instructions until al dente, about 8-10 minutes. Reserve 1 cup of pasta water, then drain the pasta in a colander.
While the pasta is cooking, heat the olive oil in a skillet over medium heat. Add the sliced chicken and season with salt and pepper. Cook for 5-7 minutes until the chicken is cooked through and golden brown. Remove the chicken from the skillet and set aside.
In the same skillet, add minced garlic and sauté for about 1 minute until fragrant.
Pour in the heavy cream and bring to a gentle simmer.
Gradually whisk in the grated Parmesan cheese until it melts smoothly into the sauce. If the sauce is too thick, add some reserved pasta water, a little at a time, to achieve the desired consistency.
Return the cooked chicken to the skillet and stir to coat the chicken with the Alfredo sauce.
Add the cooked fettuccine to the skillet and toss until the pasta is evenly coated in the sauce. Adjust seasoning with additional salt and pepper if necessary.
Serve hot, garnished with chopped parsley.