Heat the oil in a large skillet over medium heat. Cook the chopped chard stems, onion, and ginger in the hot oil until they begin to soften; season with salt and pepper. Add the chopped chard leaves to the skillet; reduce heat to low. Continue cooking until the leaves have wilted, about 2 minutes more. Drizzle the maple syrup over the mixture; stir to coat evenly. Remove from heat and serve.