Place the eggs in a saucepan and cover with cold water. Place over high heat and bring to a boil. Boil the eggs for exactly 4 minutes. Remove from the heat and let sit 10 more minute before draining. Run under cold water and peel the eggs immediately - the shell will come off much more easily while the eggs are still wet and warm.
Using a box grater, grate the eggs on the shredder side into a bowl. Add the salmon, dill, capers, 1/4 cup of the mayonnaise, salt and pepper. Mix well.
Lay out 7 slices of the bread and spread 1/4 cup of the egg salad onto each slice. Cover with the remaining bread slices. Trim the crust off of all the sandwiches and cut each sandwich crosswise into four triangles.
Spread the long side of each triangle with a little mayonnaise and dip each one into the chopped chives. Arrange decoratively on a platter.