Preheat your oven to 400°F and line a large baking sheet with parchment paper for easy cleanup.
Peel and chop the carrots and parsnips into uniform 1-inch chunks, and slice the red onion into thick wedges.
In a large mixing bowl, toss the vegetables with half of the olive oil, half of the minced garlic, rosemary, salt, and pepper.
Spread the seasoned vegetables in a single layer on the prepared baking sheet.
Rub the chicken breast with the remaining olive oil, garlic, salt, and pepper until evenly coated.
Place the chicken breast in the center of the sheet pan, nestling it among the root vegetables.
Roast for 20 to 25 minutes, or until the chicken reaches an internal temperature of 165°F and the vegetables are fork-tender.
Remove from the oven and let the chicken rest for 5 minutes before slicing to ensure the juices redistribute.