In a medium pot, boil enough water to cover the eggs by at least one inch. When the water comes to a boil, reduce the heat so you have a low simmer (just barely bubbling). If the water is bubbling too much, you’ll risk cracking the eggs when you place them in the pot.
Carefully lower the eggs one at a time into the simmering water with a slotted spoon. Simmer gently for 18 minutes (or 16 minutes if the eggs are starting at room temperature).
After cooking, remove the eggs from the water and submerge them in a bowl of cold water. Once they’re ready to handle, you can peel them. Tap each egg on the counter, then roll it while pressing gently. This should allow you to remove the peel easily. Rinse the eggs to avoid leaving any little bits of shell on them.
Cut each egg in half and remove the yolks to a bowl. Add the yogurt, mayonnaise, mustard, and 1 teaspoon of chives to the yolks. Stir to combine evenly. If the mixture is too thick, add a teaspoon or two of water until it’s creamy.
Taste the yolk mixture, and add a bit of salt if you think it needs it.
Pipe the yolk mixture into the egg white halves, or scoop the mixture into the eggs with a spoon.
Garnish with the remaining chives. Refrigerate until ready to serve.