Heat the wine in a large skillet over medium heat. Add the sole, drizzle with the oil, and season with 1/4 teaspoon salt and 1/8 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 individual plates, spooning the wine and caper sauce over the top.