Bring a large pot of salted water to a boil. Add the fettuccine and cook according to the package instructions until it reaches al dente texture. Before draining, reserve about half a cup of pasta water just in case you need to thin out your sauce later.
While the pasta is cooking, heat the olive oil in a large skillet over medium-high heat. Season the chicken strips with salt and pepper. Add the chicken to the skillet and cook for 5 to 7 minutes until golden brown and cooked through. Remove the chicken from the pan and set it aside.
In the same skillet, reduce the heat to medium and add the butter. Once melted, add the minced garlic and sauté for about 1 minute until fragrant. Pour in the heavy cream and let it come to a gentle simmer. Whisk in the grated Parmesan cheese slowly until the sauce becomes smooth and slightly thickened.
Add the cooked pasta and the sautéed chicken back into the skillet with the sauce. Use tongs to toss everything together until the noodles are fully coated. If the sauce is too thick, add a splash of the reserved pasta water. Garnish with fresh parsley and extra Parmesan before serving.