Prepare all of the ingredients. Start water boiling for pasta.
Sprinkle both sides of chicken with seasonings. In large saute pan over medium-high heat, add oil. Cook chicken for 8-9 minutes on each side. Remove to plate and keep warm.
Add pasta to boiling water and cook as directed on package. Drain in colander and rinse with cool water to arrest cooking process. Return to pot and add butter, garlic, parsley and parmesan cheese. Toss to coat.
Add butter and oil for sauce to saute pan. Add onions, garlic and parsley. Cook until butter is fully melted. Whisk in flour and cook for 3 minutes. Whisk in chicken broth and cook for 3 minutes. Whisk in balsamic vinegar and cook for 2 minutes then add heavy cream and cook another 2 minutes.
To plate, place a portion of pasta to one side of plate. Take a piece of chicken and dunk it in balsamic sauce and place on other side of plate. Ladle additional sauce down center of plate and garnish with additional parmesan, if desired.