Wrap each piece of salmon loosely in plastic film. Place on a work surface and using a meat pounder or mallet, pound the fish gently to about 1/8-inch thickness.
Unwrap the salmon and transfer each flattened fillet to a serving plate. Season the fish lightly with salt and pepper and sprinkle with the chives.
In a small skillet over high heat, heat the olive oil until very hot, about 5 minutes. Stir in the ginger, remove from the stove, and immediately spoon a bit of the oil over 1 portion of the fish. The fish should sizzle when the oil hits it; if not, return the skillet to the stove, reheat the oil. Spoon 1 tablespoon of the hot oil over each portion and serve at once.