In a large skillet (one that will fit all the liquid and the pasta), heat oil over medium-high heat and brown chicken, roughly 2-3 minutes per side.
Add garlic and cook 1 minute.
Add broth, salt and pepper, and scrape and bits off the bottom of the pan with a wooden spoon.
Add fettuccine and stir well, pressing all of the pasta into the liquid. Bring to a simmer and reduce heat to medium low. Cover and cook until most of the liquid is absorbed and pasta is nearly cooked.
Stir in heavy cream and Parmesan. Cook over medium heat until it reaches a simmer and thickens slightly. Serve.