Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Wash and dice the potato into 1-inch cubes, then toss them in a bowl with 0.5 tbsp of olive oil, sea salt, and black pepper.
Spread the potatoes in a single layer on the baking sheet and roast for 15 minutes.
While potatoes roast, rub the chicken breast with the remaining 0.25 tbsp of olive oil, dried oregano, garlic powder, and dried thyme.
Remove the baking sheet from the oven, push the potatoes to one side, and add the chicken breast and broccoli florets to the empty space.
Return the sheet to the oven and bake for an additional 18 to 20 minutes, or until the chicken reaches an internal temperature of 165°F and the potatoes are golden brown.
Let the chicken rest for 5 minutes before slicing and serving alongside the roasted vegetables.