Cook the pasta according to the package instructions until al dente. Drain and set aside.
In a large skillet, heat the olive oil over medium heat. Season the chicken pieces with salt and pepper, then add them to the skillet. Cook until the chicken is browned and cooked through, about 6-8 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the chopped onion and cook until softened and translucent, about 3-4 minutes. Add the minced garlic and cook for an additional 1 minute, until fragrant.
Pour the heavy cream into the skillet, stirring to combine with the onion and garlic. Bring the mixture to a simmer, then reduce the heat to low and cook for 3-4 minutes, until slightly thickened.
Stir in the prepared pesto and grated Parmesan cheese, mixing until well combined and the cheese has melted.
Add the cooked pasta and chicken to the skillet, tossing everything together to ensure the pasta and chicken are evenly coated in the creamy pesto sauce.
Cook for an additional 2-3 minutes, until heated through. Season with additional salt and pepper if needed.
Serve your Creamy Pesto Chicken Pasta in bowls, garnished with chopped fresh basil or parsley if desired.