Heat oil in a Dutch oven over medium heat. Add chard stems, salt and pepper and cook, stirring often, until softened, 3 to 5 minutes. Stir in chard leaves and cook, stirring constantly, until wilted, about 2 minutes. Stir in olives and currants. Dot goat cheese over the top, cover and cook until the chard is tender and the cheese is melted, about 2 minutes more.
Note: After washing the chard for these recipes, allow some of the water to cling to the leaves. It helps steam the chard and prevents a dry finished dish.