Heat the wine in a large skillet over medium heat. Add the sole, drizzle with the oil, and season with ¼ teaspoon salt and ⅛ teaspoon pepper.
Sprinkle the capers over the top and cook, covered, until just cooked through, opaque, and beginning to flake, about 4 minutes.
Sprinkle with the chives. Divide among plates, spooning the wine-and-caper sauce over the top.