Preheat your oven to 400°F and line a large baking sheet with parchment paper for easy cleanup.
Cut the chicken breast into 1-inch pieces and dice the red potatoes into 1/2-inch cubes to ensure even cooking.
In a large mixing bowl, whisk together the olive oil, lemon juice, lemon zest, oregano, garlic powder, sea salt, and black pepper.
Add the chicken and potatoes to the bowl, tossing well to ensure every piece is thoroughly coated in the herb mixture.
Spread the chicken and potatoes onto the sheet pan in a single layer, leaving space for air to circulate.
Roast for 15 minutes, then remove the pan and add the broccoli florets, tossing them quickly with the existing juices.
Return the pan to the oven for an additional 12 minutes until the chicken is cooked through and the potatoes are golden and tender.