In a very large soup pot, heat the olive oil. Add the garlic and cook over moderately high heat, stirring, just until fragrant, about 30 seconds. Add the chicken stock, then add the kale in large handfuls, letting it wilt slightly before adding more. Season with salt and pepper, cover and cook over moderate heat until the kale is tender, about 5 minutes.
Remove the lid and cook until the liquid has evaporated, about 3 minutes longer. Transfer to a bowl and serve.
The braised kale can be covered and refrigerated overnight. Reheat before serving.