Preheat your oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper for easy cleanup.
Cut the chicken breast, sweet potato, and zucchini into uniform 1-inch cubes to ensure they cook at the same rate.
In a small mixing bowl, whisk together the olive oil, lemon juice, minced garlic, rosemary, thyme, sea salt, and black pepper.
Place the chicken cubes, sweet potato, zucchini, and broccoli florets onto the prepared baking sheet.
Drizzle the lemon-herb oil over the ingredients and toss thoroughly with your hands or tongs until every piece is well-coated.
Spread the mixture into a single layer, making sure the chicken and vegetables are not overcrowded so they roast rather than steam.
Roast for 20 to 25 minutes, tossing halfway through, until the chicken is cooked through and the vegetables are tender and golden brown.