Heat the oil in a large skillet over medium heat. Add the garlic and cook, stirring, until golden, 2 to 3 minutes.
Add the chard, ½ teaspoon salt, and ¼ teaspoon pepper. Cook, tossing occasionally, until the chard is tender, 4 to 5 minutes.
Meanwhile, in a medium saucepan, bring 4 cups of water to a boil. Add 1 tablespoon salt.
Slowly whisk in the polenta and cook, whisking constantly, until it thickens, 3 to 4 minutes.
Divide the polenta among bowls and top with the chard and blue cheese.