Preheat the oven to 425°F (220°C).
Prepare the vegetables by peeling (if desired) and cutting the carrot, parsnip, and sweet potato into uniform bite-sized pieces.
In a bowl, toss the vegetables with olive oil, a pinch of salt, pepper, and finely chopped rosemary and thyme.
Place the vegetables on a baking sheet in a single layer and roast in the oven for about 15 minutes.
Meanwhile, pat the chicken breast dry and season generously with salt, pepper, and additional chopped rosemary and thyme.
After the vegetables have roasted for 15 minutes, remove the baking sheet and nestle the chicken breast among the vegetables. Return the sheet to the oven.
Roast everything together for an additional 15-20 minutes, or until the chicken is cooked through (internal temperature reaches 165°F) and the vegetables are tender with a crispy edge.
Remove from the oven, let the chicken rest for a few minutes, slice if desired, and serve the chicken alongside the roasted root vegetables.