Bring a large pot of lightly salted water to a boil. Add pasta and cook for 8 to 10 minutes or until al dente; drain.
Heat butter and olive oil in a large frypan over medium heat. Saute chicken and garlic until chicken is almost cooked. Reduce heat and stir in salt, pepper, cream, pesto and Parmesan cheese. Cook until chicken is no longer pink inside. Stir in cooked pasta.