Combine all marinade ingredients in a small bowl and whisk well to combine.
Place chicken in a shallow dish and drizzle with about half of the marinade.
Let marinade for 30 minutes, or up to overnight.
If you are marinating overnight, save the rest of the marinade in an airtight container in the refrigerator for the veggies.
Preheat oven to 400 degrees F.
Place squash in a large microwave safe bowl and microwave on high for 2 minutes.
Add brussels sprouts to bowl and toss in remaining marinade.
Grease a large baking pan with cooking spray or olive oil.
Place chicken breasts on baking dish and then arrange the veggies around the chicken. If your baking dish is not large enough for it all, you may need to use a second pan for the rest of the veggies.
Bake in preheated oven for 30-40 minutes, depending on how thick your chicken breast is cooked through. The best way to do this is to use a meat thermometer, and bake until chicken is 165 degrees in the thickest part. The squash will need at least 30 minutes of baking.
Serve with balsamic reduction. Enjoy!