Cook the fettuccine pasta in a large pot of salted boiling water until al dente, according to the package instructions.
Meanwhile, heat the olive oil in a large frying pan over medium-high heat. Add the chicken breast pieces and season with salt and black pepper. Cook until golden brown and fully cooked, about 6-8 minutes.
Remove the chicken from the pan and set aside. In the same pan, add the unsalted butter and crushed garlic, cooking for about 1 minute until fragrant.
Pour in the double cream and bring to a simmer. Stir in the grated Parmesan cheese until melted and the sauce is smooth.
Return the chicken to the pan and stir to coat in the sauce. Drain the pasta and add it to the pan, tossing everything together until the pasta is well coated.
Serve the Chicken Alfredo hot, garnished with freshly chopped parsley and additional black pepper if desired.