Cook pasta according to package directions; drain and set aside.
Season chicken slices 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 4-5 minutes per side. Remove and set aside.
In the same skillet, sauté minced garlic until fragrant, about 1 minute.
Pour in chicken broth and bring to a simmer, scraping up browned bits from the skillet.
Add heavy cream, Parmesan, lemon zest, and lemon juice. Stir until the sauce thickens slightly, about 2-3 minutes.
Return chicken to the skillet, along with the cooked pasta. Toss everything together to coat well.
Garnish with fresh parsley and serve immediately.