Preheat your oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper.
Peel the carrots and parsnips, then chop them into uniform 1-inch pieces; slice the red onion into thick wedges.
In a mixing bowl, toss the carrots, parsnips, and onions with half of the olive oil and a pinch of the salt and pepper.
Mince the garlic and finely chop the fresh rosemary leaves.
Pat the chicken breast dry with a paper towel and rub with the remaining olive oil, minced garlic, rosemary, and the rest of the salt and pepper.
Spread the vegetables in a single layer on the prepared baking sheet and nestle the chicken breast in the center.
Roast for 25 to 30 minutes, or until the chicken reaches an internal temperature of 165°F and the vegetables are tender and golden brown.
Remove from the oven and let the chicken rest for 5 minutes before slicing to keep it juicy.
Serve the sliced chicken alongside the roasted root vegetables.