Cook penne pasta according to package instructions. Drain and set aside.
Add butter and oil to a large skillet over medium heat. Add chicken and cook for a few minutes until golden on bottom, flip over and cook another few minutes until cooked through.
Stir in heavy cream, pesto, parmesan cheese, and sun dried tomato. Simmer over low heat for a few minutes until sauce lightly thickens. Add penne pasta and toss to combine.