Roughly chop the kale leaves into 1-inch pieces, then wash and drain throughly. In a large skillet, heat the olive oil 2 minutes. Add the garlic and lightly brown, then immediately add the kale. Turn the kale leaves to coat evenly with the olive oil and to prevent the garlic from burning on the bottom of the pan. Season with salt and pepper.
Continue to saute the kale leaves 3 to 4 minutes. Reduce the heat to medium and add the chicken stock. Cover the pan and cook the kale in the stock 5 minutes more. Remove the cover, add the red wine, and continue to braise the kale in the red wine and stock until nearly all of the liquid has evaporated. The entire cooking process will take 12 to 15 minutes, at which time the kale should be tender and the liquid cooked off.