Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Wash the Yukon gold potato and cut it into 1-inch cubes. Mince the garlic cloves.
In a large bowl, toss the potato cubes with half of the olive oil, half of the minced garlic, rosemary, thyme, salt, and pepper.
Spread the potatoes in a single layer on the baking sheet and roast for 15 minutes.
While potatoes roast, cut the chicken breast into 1-inch bite-sized pieces and toss them in the same bowl with the remaining olive oil, garlic, and broccoli florets.
Remove the baking sheet from the oven, add the chicken and broccoli to the tray, and toss everything together.
Return the tray to the oven and roast for an additional 15 to 20 minutes, or until the chicken is cooked through and the potatoes are golden brown.
Serve immediately while the potatoes are hot and crispy.