Have a bowl of ice water big enough to hold the eggs ready.
Cover eggs with cold water by ½ an inch. Bring to a gentle boil.
Turn off the heat, cover, and let sit for 7 minutes.
When the eggs are done cooking place them in the ice bath for 3 minutes. The key is to avoid over cooking, and to dunk the eggs in a bowl of ice water to stop the cooking after you remove them from the hot water.
Crack and peel each egg; place in a mixing bowl.
Add the mayonnaise, salt and pepper to taste; mash with a fork. Do not over-mix. Eggs should still have some texture.
Stir in the celery and chives. Variation: I sometimes use celery salt for the flavor and skip the chives. I also like to add just a single slice of raw onion, diced very fine.
Assemble your sandwiches. Between pieces of toast place a leaf of lettuce topped with egg salad. I like to cut these diagonally while I'm assembling. Variation: a friend insists that a slice of tomato is required before this sandwich is complete. Not for me, but you might like it!