Place eggs in a large saucepan and cover with cold water. Set pan over medium-high heat and bring water to a boil. Turn off heat, cover pan with a lid and let sit for 11 minutes. Drain, rinse eggs under cold water and peel.
Halve eggs crosswise and scoop out yolks into a medium bowl. Add mayonnaise, hot sauce, and Dijon mustard to bowl, then mash yolks with the back of a fork and stir until mixture is smooth. Season with salt and pepper.
Using a small cookie or ice cream scoop, scoop mixture into each egg. Garnish with chives and paprika and serve.