Cook the fettuccine according to package instructions until al dente. Drain and set aside.
In a large skillet, heat olive oil over medium heat.
Season the chicken breasts with salt and pepper, and add them to the skillet.
Cook the chicken for about 6-7 minutes on each side until fully cooked. Remove and let rest.
In the same skillet, melt butter and add minced garlic, sautéing until fragrant.
Pour in the heavy cream, stirring constantly until it starts to simmer.
Gradually add the Parmesan cheese, whisking until the sauce is smooth.
Add the cooked broccoli florets to the skillet, mixing well with the sauce.
Slice the chicken and add it back to the skillet, along with the cooked fettuccine.
Toss everything together until well coated in the Alfredo sauce, then serve hot.