Heat olive oil in a large pot over medium heat. Add chicken and cook until golden on all sides.
Stir in garlic and cook for 30 seconds until fragrant.
Pour in chicken broth and bring to a gentle boil.
Add pasta and cook according to package instructions, stirring occasionally until tender.
Reduce heat to low, stir in heavy cream and pesto, and season with salt and pepper.
Simmer for 2 minutes until the sauce thickens slightly.
Serve topped with grated Parmesan and fresh basil.