In a large bowl, combine the tomatoes with their juices, garlic, salt, vinegar, 1 tablespoon of the olive oil and half the basil. Cover and let sit for 30 minutes or longer. Stir, taste, adjust salt and add pepper.
Meanwhile, wilt chard by blanching in boiling salted water for about a minute or by steaming above 1 inch of boiling water for about 2 to 3 minutes, flipping the bunch top to bottom using tongs halfway through. Transfer to a bowl of cold water, drain and squeeze out excess water, taking up the chard by the handful. Chop coarsely.
Heat the remaining tablespoon of olive oil in a large skillet over medium heat. Add chard and heat through, stirring, until coated with oil. Season to taste with salt and pepper.
Remove to a platter or to plates, spoon on the tomato sauce, sprinkle the remaining basil over the top and serve.
Recipe Notes
Adapted from Cooking NY Times (www.cooking.nytimes.com)