Heat the oil in a large skillet over medium-high heat. Season the pork with ½ teaspoon each salt and pepper and cook until browned and cooked through, 7 to 9 minutes per side. Transfer to a plate and tent with foil to keep warm; reserve the skillet.
Add the apples and onion to the drippings in the skillet and cook over medium-high heat, tossing frequently, until slightly softened, 6 to 8 minutes. Add the broth, vinegar, and sugar and cook, tossing occasionally, until thickened, 3 to 4 minutes. Add 1 tablespoon of the butter. Return the pork chops to the skillet and cook until warmed through, 1 to 2 minutes.
Meanwhile, in a medium saucepan, bring 3 cups of water to a boil. Whisk in the polenta and cook, whisking, until thickened, 3 to 4 minutes. Whisk in the remaining 2 tablespoons of butter, ½ teaspoon salt, and ⅛ teaspoon pepper. Top the polenta with the pork chops and apple mixture and sprinkle with the chives.
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