Wash the chard well in a large bowl or sink filled with water. Lift the chard out of the water, give it a good shake to remove excess water, and transfer it to a cutting board. Coarsely chop the stems and slice the leaves crosswise into ribbons, keeping the stems and leaves in separate piles.

Heat the oil and garlic together in a large skillet over medium heat, stirring often, just until the garlic begins to soften, about 1 minute. Add the anchovies (or anchovy paste) and red pepper flakes and let them sizzle for a few seconds. Stir in the chard stems, reduce the heat to medium-low, and cook until the stems are beginning to soften, about 3 minutes. In 2 or 3 batches, stir in the chard leaves, letting each batch wilt before adding more. Stir in the tomatoes and olives and cook until heated through. Season with salt and serve hot.