Whisk first 6 ingredients in medium bowl to blend. Whisk buttermilk, egg, and chile in small bowl to blend. Stir buttermilk mixture and cheese into dry ingredients.
Add enough oil to deep medium saucepan to reach 1 1/2 inches. Attach deep-fry thermometer to pan; heat oil to 320°F to 330°F over medium heat. Working in batches of 4 or 5, drop batter by tablespoonfuls into oil. Cook until golden, turning occasionally, about 4 minutes. Using slotted spoon, transfer hush puppies to paper towels. DO AHEAD: Can be made 2 hours ahead. Let stand at room temperature. Rewarm until crisp in 375°F oven, 12 to 14 minutes.