Place chard on a flat work surface. Remove large stems and cut into 1/2-inch slices. Chop leaves coarsely.
Heat oil in a saucepan over medium heat. Add ginger; cook and stir until fragrant, about 1 minute. Add chard stems; cook until tender, about 5 minutes. Toss in chard leaves and season with salt; cook and stir until chard is wilted and liquid is mostly reduced, about 5 minutes.