Cook pasta according to package instructions for the "firm" degree of doneness. Add broccoli florets for the last two minutes of cooking. Reserve 1 cup of the starchy cooking water. Drain pasta and broccoli. Return pasta and broccoli to hot pot add reserved cooking water and set aside, keeping warm.
Heat olive oil over medium high heat in a large skillet.
Once hot, add onion and garlic and cook for 3-4 minutes or until the onion is soft and is starting to turn translucent.
Add chicken and cook until the chicken is cooked through (approximately 5 minutes).