Bring a large pot of salted water to a boil. Add the Swiss chard and cook until tender, about 3 minutes. Drain the chard and, when cool enough to handle, gently press out any excess water. Coarsely chop the chard.
In a large skillet, melt 2 tablespoons of the butter. Add the onion and season with salt. Cover and cook over low heat, stirring a few times, until the onion is translucent, about 5 minutes. Stir in the chard, cover and cook, stirring a few times, until heated through, about 3 minutes. Add the tomato puree and stir until hot. Remove from the heat and stir in the remaining 2 tablespoons of butter. Season with salt and pepper and serve.