Preheat the oven to 400 degrees F. Line a baking sheet with a layer of paper towels.
Drain the peels and tip onto the paper towel-lined baking sheet. Dry the peels thoroughly, then discard the paper towels. Pour over the butter, oil, kosher salt, pepper, paprika and oregano and toss.
Roast, stirring once, until crisp and golden, about 20 minutes. Tip the peels into a serving dish, sprinkle over the chives and sea salt and toss.