Prepare the Swiss chard: use a sharp paring knife to remove the thick stems from the chard, then thinly slice the stems. Set aside in a pile. Coarsely chop the chard leaves, and set aside in a separate pile.
Bring a large pot of water to a boil, then add the potatoes.
After 20 minutes, add the sliced chard stems to the pot of boiling water. Cook the stems for 10 minutes, then add the chard leaves and boil for another 5 minutes. Drain in colander.
Heat 2 tablespoons of the olive oil in a large skillet over medium heat. Add the garlic, cook about 1 minute until the begins to brown.
Add the cooked chard and potatoes, season lightly with salt and pepper. Cook, stirring and gradually mashing the potatoes, until the liquid is absorbed and the potatoes are coarsely mashed. Add the remaining 2 tablespoons of olive oil, season to taste with salt and pepper. Stir to combine the added olive oil and seasonings. Serve and enjoy as a substantial side dish.