Cook pasta according to package directions. Drain and set aside.
Season chicken pieces with salt and pepper.
Heat olive oil in a large skillet over medium-high heat. Add chicken and cook until browned and cooked through. Remove chicken from the skillet and set aside.
Reduce heat to medium. Add minced garlic to the skillet and cook for 1 minute until fragrant. Do not let it burn.
Pour in heavy cream and chicken broth. Bring the mixture to a gentle simmer, stirring occasionally.
Reduce heat to low. Stir in the grated Parmesan cheese until the sauce is smooth.
Return the cooked chicken to the skillet. Add the cooked pasta. Toss everything together until the pasta and chicken are coated with the sauce.
Serve immediately, garnished with fresh parsley.
Notes
For a thicker sauce, simmer the cream and broth mixture for an extra 2-3 minutes before adding cheese.
You can substitute half-and-half for heavy cream for a slightly lighter sauce, but the texture will be less rich.