Rinse Swiss chard well. Trim tough ends; slice stalks about 3/4 inch thick. Slice leaves about 1 inch thick.
In a Dutch oven over medium heat, warm olive oil. Cook garlic until fragrant, 1 to 2 minutes.
Stir in stalks; cook, stirring, until slightly soft, 5 to 6 minutes. Add half the leaves; sprinkle with 1 teaspoon sugar. Cover; cook until wilted, about 4 minutes. Add remaining leaves; sprinkle with another teaspoon sugar. Cover; cook, tossing occasionally, until leaves are tender, 8 to 10 minutes.
Uncover; cook until liquid has evaporated, about 2 minutes. Stir in red-wine vinegar; season with coarse salt and ground pepper.
Swiss chard is in the same family as spinach and beets. Its leaves are green, but the ribs and stalks can be a variety of colors -- white, red, yellow, and orange or sold together as "rainbow chard."