Heat oven to 425°. Cut off green radish tops and cut radishes in half lengthwise if large. Place radishes in a lightly oiled cast iron skillet; sprinkle lightly with salt. Roast until crisp-tender and lightly browned, stirring occasionally, 20–25 minutes.
Remove from oven and add butter, lemon zest, and chives to skillet, tossing to coat radishes. Finish with lemon juice and sea salt to taste. Serve warm in skillet.