Place the eggs in a large pot and add enough cold water to cover completely + 1 inch.
Put the pot on a burner over medium-high heat and bring the water to a boil. As soon as the water is at a rolling boil, turn off the heat and cover the pot with a tight fitting lid.
Allow the eggs to continue to cook in the hot water for next 10 to 12 minutes.
Remove a grill rack from your smoker.
Fill the water bowl of the smoker 1/2 way. Add wood chips to the tray or pellets to the hopper.
Following the manufacturer’s instructions, heat the smoker to between 200°F and 225°F with the top vent open.
Fill a large bowl with icy cold water. Using a slotted spoon, remove the eggs from the pot and place them in the bowl of cold water to stop the cooking.
When the eggs are cool enough to handle, peel each one and return each egg to the bowl of cold water until you have finished peeling all of them.
Using the slotted spoon, remove the eggs to paper towels to drain.
Lightly oil the smoker rack. Place the eggs on the rack in the voids between each grate so that they don’t roll around.
Place the rack inside the smoker and cook the eggs for approximately 25 to 35 minutes until they are a light bronze color.
Remove the smoked eggs to a clean cutting board. Slice them in half lengthwise.
Using a teaspoon, gently scoop out the yellow yolks and place them in a dry mixing bowl.
Add the mayonnaise, relish, mustard, salt, and pepper and mix very well until you have a creamy consistency.
Using the spoon or a piping bag, fill the cavities of each egg white half with the yolk mixture.
Be generous so the filling has some height above the whites.
Place the filled egg halves on a platter and chill them in the refrigerator until cool or cold.
Before serving, scatter some chives over the top of each egg. Then, dust with a little paprika. Serve with cocktail napkins and enjoy.