Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper for easy cleanup.
Wash the russet potato and dice into 1/2-inch cubes; slice the chicken breast into similar bite-sized pieces to ensure even cooking.
In a large mixing bowl, combine the chicken and potatoes with olive oil, sea salt, black pepper, dried rosemary, garlic powder, and onion powder, tossing until thoroughly coated.
Spread the mixture in a single layer on the prepared baking sheet, making sure the pieces are not crowded so they roast rather than steam.
Roast for 22-25 minutes, tossing halfway through the cooking time, until the potatoes are golden and the chicken is cooked through.
While the chicken and potatoes finish roasting, steam the broccoli florets in a steamer basket for 4-6 minutes until tender-crisp.
Divide the roasted chicken and potatoes onto a plate and serve immediately with the steamed broccoli.