Heat a large cast iron (or other heavy) skillet over medium. Working in two batches, add the damp chard and cook, tossing it with tongs, until wilted, about 3-4 minutes. Transfer to a bowl.
Season the chicken with the salt, marjoram and pepper.
Heat 1 tablespoon of the oil in the skillet over medium heat. Add the chicken (skinner/smooth side facing down) and cook until golden brown, 6-7 minutes. Turn it over and add the potatoes to the pan around the chicken. Cook until the chicken is again browned on the underside, about 6 minutes.
Pour the broth and vinegar into the pan and cook until it is slightly thickened, about 1 minute. Place the chard over the potatoes, drizzle with the remaining 1 tablespoon olive oil, and cook until the potatoes are tender and the chicken is cooked through (to an internal temperature of 170-175F, about another 15 minutes.
341 calories, 25 g protein, 25 g carbohydrates, 3 g fiber, 16 g fat, 3 g saturated fat, 552 mg sodium