Preheat your oven to 400°F (200°C) and line a large sheet pan with parchment paper for easy cleanup.
Wash and dice the red potatoes into 1-inch cubes and peel and slice the carrots into 1/2-inch thick rounds.
Trim the ends of the green beans and set them aside separately from the root vegetables.
In a large bowl, toss the potatoes and carrots with half of the olive oil, rosemary, garlic powder, salt, and pepper.
Spread the potatoes and carrots in a single layer on the prepared sheet pan and roast for 15 minutes.
While the vegetables roast, rub the chicken breast with the remaining olive oil and seasonings.
Remove the pan from the oven, toss the green beans with the root vegetables, and move them to the sides to make room for the chicken.
Place the chicken breast in the center of the pan and return to the oven for another 15-20 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.