In a large skillet, heat oil over medium-high heat. Add the onions and cook for about 3 minutes, add the garlic, and continue cooking until the onions have softened.
Add the chicken pieces to the pan and cook, for about 5 minutes, long enough to sear on all sides.
Slowly pour in the chicken broth and cream and scrape the tidbits from the chicken left at the bottom of the pan while stirring.
Bring mixture to a boil, add the pasta, and mix to combine. Reduce heat to low, cover the pan with the lid, and simmer for 12 to 15 minutes until the pasta is tender.
Open the lid, stir in the pesto until incorporated and heated through. Turn off the heat, add the parmesan cheese, stir to combine, and serve.