Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Chop the potato into 1-inch cubes and slice the carrots into rounds.
In a small bowl, whisk together the olive oil, lemon juice, lemon zest, minced garlic, rosemary, salt, and pepper.
Place the chicken breast, potatoes, and carrots on the baking sheet and drizzle with two-thirds of the lemon-herb mixture, tossing to coat.
Roast for 15 minutes, then add the broccoli florets to the tray and drizzle with the remaining sauce.
Continue roasting for another 10-12 minutes until the chicken reaches an internal temperature of 165°F and the vegetables are fork-tender.
Let the chicken rest for 5 minutes before slicing and serving with the roasted vegetables.