Heat oven to 425° F. On a rimmed baking sheet, toss the potatoes with the oil; season with ½ teaspoon salt and ¼ teaspoon pepper. Roast until golden and tender, 40 to 45 minutes.
Meanwhile, in a large nonstick skillet, cook the chorizo and onion over medium heat until the onion is soft, 5 to 6 minutes.
In a medium bowl, beat the eggs with ¼ teaspoon each salt and pepper. Add to the skillet and cook, stirring, until set but still soft, 2 to 3 minutes. Sprinkle with the chives and serve with the potatoes.