Heat 1 tablespoon of the oil in a large skillet over medium-high heat.
Add the sausage and cook, turning occasionally, until cooked through, 10 to 12 minutes. Transfer to a cutting board and let rest 5 minutes before slicing.
Cook the polenta according to the package directions.
Meanwhile, wipe out the skillet and heat the remaining tablespoon of oil over medium heat. Add the garlic and cook, stirring for 1 minute.
Add the Swiss chard, ½ teaspoon salt, and ¼ teaspoon pepper and cook, tossing, until wilted, 3 to 4 minutes. Fold in the sliced sausage.
Serve the sausage and chard mixture over the polenta.