Bring a large pot of salted water to a boil and cook the fettuccine according to package directions until al dente; drain and set aside.
While the pasta cooks, slice the chicken breast into thin strips and pat dry.
Heat the olive oil in a large nonstick skillet over medium heat. Add the chicken strips and cook until golden and cooked through, about 6–7 minutes per side depending on thickness. Transfer the cooked chicken to a plate and set aside.
In the same skillet, add the minced garlic and sauté for about 1–2 minutes until fragrant (do not let it burn).
Pour in the chicken broth and add the lemon juice, scraping up any browned bits from the pan. Bring the mixture to a gentle boil.
Reduce heat to low and stir in the heavy cream. Simmer gently for 2–3 minutes to warm the cream and thicken slightly.
Add the cooked pasta and the chicken back to the skillet and toss to combine and heat through.
Remove the pan from heat and stir in the grated Parmesan until the sauce is smooth and coats the pasta. Season to taste with salt and pepper if desired.
Sprinkle with chopped fresh parsley and serve immediately.