Heat oil in a large skillet over medium-high. Add chard stems, shallots, and garlic and season with salt. Cook, stirring occasionally, until vegetables are starting to soften but haven’t taken on any color, about 2 minutes. Add chard leaves, season with salt, and cook, tossing occasionally, until leaves are tender and have released some liquid, about 3 minutes (stems will have a bit of crunch). Mix in vinegar; taste and season with more salt if needed.