In a large skillet, heat olive 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. Slowly pour in the chicken broth and cream.
Cook the pasta:
Bring the 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. When the pasta is nearly done but a little tough, add the cooked chicken to the pasta.
Add pesto:
Open the lid, stir in the pesto until incorporated and heated through.
Serve:
Turn off the heat, add the parmesan cheese, stir to combine, and serve.