Cook the Fettuccine: Fill a large pot with water, add salt, and bring it to a boil. Cook the fettuccine pasta according to the package instructions until it's all dente. Drain the pasta and set it aside.
Cook the Chicken: In a skillet or frying pan, heat olive oil over medium heat. Add the sliced chicken breasts and season them with salt and pepper. Cook the chicken until it's golden brown and cooked through, about 6-8 minutes. Remove the cooked chicken from the skillet and set it aside.
Prepare the Sauce: In the same skillet, add minced garlic and cook it for about 1 minute until it becomes fragrant. Pour in the chicken broth and heavy cream, stirring to combine. Let the mixture simmer for about 5 minutes to slightly thicken.
Add Parmesan Cheese: Gradually stir in the grated Parmesan cheese, continuing to stir until the cheese has melted and the sauce is smooth and creamy.
Combine Chicken and Sauce: Return the cooked chicken to the skillet, stirring it into the Alfredo sauce. Let it simmer for a few more minutes to heat the chicken through and allow the flavors to meld.
Serve: Serve the Chicken Alfredo over the cooked fettuccine pasta. Garnish with chopped parsley if desired.
Enjoy: Serve the Chicken Alfredo hot and enjoy your delicious homemade meal.