Preheat your oven to 400°F (200°C) and line a large sheet pan with parchment paper for easy cleanup.
Peel the carrots and parsnips, then chop them into 1-inch chunks; slice the red onion into thick wedges.
In a large mixing bowl, toss the prepared vegetables with 0.5 tbsp of olive oil, half of the minced garlic, and a pinch of salt and pepper.
Pat the chicken breast dry with a paper towel and rub it thoroughly with the remaining 0.5 tbsp of olive oil, garlic, rosemary, thyme, salt, and pepper.
Spread the seasoned vegetables in a single layer on the sheet pan and place the chicken breast in the center.
Roast in the oven for 20 to 25 minutes, or until the chicken reaches an internal temperature of 165°F and the vegetables are tender and lightly browned.
Remove from the oven and let the chicken rest for 5 minutes before slicing to ensure the juices redistribute.
Plate the sliced chicken alongside the roasted root vegetables and serve immediately.