Preheat your oven to 425°F (220°C) and line a large rimmed baking sheet with parchment paper for easy cleanup.
Wash the gold potato and dice it into uniform 1/2-inch cubes; slice the chicken breast into even 1-inch strips to ensure they cook at the same rate.
In a large mixing bowl, whisk together the extra virgin olive oil, fresh lemon juice, smoked paprika, garlic powder, onion powder, sea salt, black pepper, and dried oregano.
Add the diced potatoes and chicken strips to the bowl, tossing thoroughly until every piece is well-coated in the spice and oil mixture.
Spread the chicken and potatoes in a single layer on the prepared baking sheet, making sure they aren't crowded so they can roast rather than steam.
Bake for 20 to 25 minutes, flipping the pieces halfway through, until the potatoes are golden-brown and the chicken is cooked through to an internal temperature of 165°F.
Arrange a bed of fresh baby arugula on a plate and top with the hot roasted chicken and potatoes, allowing the greens to slightly wilt from the heat.