Preheat your oven to 400°F and line a large rimmed baking sheet with parchment paper for easy cleanup.
Cut the chicken breast into 1-inch bite-sized pieces and slice the carrots and zucchini into rounds.
In a large mixing bowl, whisk together the olive oil, lemon juice, lemon zest, minced garlic, oregano, thyme, salt, and pepper.
Add the chicken, broccoli florets, carrots, and zucchini to the bowl and toss thoroughly until everything is evenly coated in the herb marinade.
Spread the mixture in a single layer on the prepared baking sheet, ensuring the pieces are not overcrowded so they roast rather than steam.
Roast in the oven for 20 to 25 minutes, or until the chicken is cooked through and the vegetables are tender and slightly caramelized.