Heat oven to 375°F. Bake biscuits as directed on bag.
Meanwhile, in small saucepan, melt butter over medium heat. Stir in flour with whisk; cook 1 to 2 minutes, stirring constantly, until mixture is bubbly. Gradually stir in milk; cook 3 to 5 minutes, stirring constantly with whisk, until sauce is thickened and smooth. Remove from heat. Stir in paprika. Season with salt and pepper. Stir in chopped hard-cooked eggs.
Split warm biscuits in half; place 2 halves on each of 4 serving plates. Spoon egg sauce evenly over biscuits. Sprinkle with chives. Serve immediately.