Bring a large pot of salted water to a boil. Cook fettuccine according to package directions until al dente. Drain, reserving 1/2 cup pasta water.
While pasta cooks, season chicken strips with salt and pepper. Heat olive oil in a large skillet over medium-high heat. Add chicken and cook until golden and cooked through, about 5-6 minutes. Remove chicken and set aside.
In the same skillet, reduce heat to medium. Add garlic and sauté for 30 seconds until fragrant. Pour in heavy cream and chicken broth, stirring to scrape up any browned bits. Bring to a simmer.
Gradually whisk in Parmesan cheese until melted and smooth. Season with salt and pepper. If sauce is too thick, add reserved pasta water a tablespoon at a time.
Return chicken to the skillet. Add cooked fettuccine and toss to coat evenly. Cook for 1-2 minutes until heated through. Garnish with parsley and serve immediately.
Tips
Use freshly grated Parmesan for the best flavor and texture.
For a lighter version, substitute half-and-half for heavy cream.
Add a pinch of red pepper flakes for a spicy kick.