In a large stockpot, cover the eggs with water so they are completely submerged and bring to a boil on the stovetop. Turn off the heat, cover and let the eggs cook in the water for 20 minutes. Pour the hot water off the eggs and replace with cold water. Let the eggs sit for 5 minutes. Crack and peel the eggs, place them in a plastic bag and refrigerate until cold, at least 3 hours or overnight.
Using an egg slicer or a knife, finely chop the boiled eggs. Add to a large bowl. Add the mayonnaise, chives, mustard, salt and pepper and mix until blended. Spread the egg mixture on the bread and make sandwiches. Cut each sandwich into 3 wedges.