Cook the fettuccine according to package instructions until al dente.
Heat olive oil in a large skillet over medium heat.
Season the chicken breast with salt and pepper, then add to the skillet.
In the same skillet, add minced garlic and sauté for about 30 seconds until fragrant.
Add the chopped roasted red peppers and heavy cream to the skillet; stir to combine.
Stir in the goat cheese and Parmesan cheese, allowing them to melt into the sauce.
Add the cooked fettuccine to the skillet, tossing to coat the pasta evenly with the sauce.
Slice the cooked chicken and place it on top of the pasta; garnish with fresh basil if desired.