Line 2 baking sheets with parchment paper or a silicone baking mat or grease the baking sheets.
Put the water and butter in a medium saucepan. Place the saucepan over high heat and bring it to a rolling boil. Add flour all at once along with a dash of salt. Stir constantly with a wooden spoon until the mixture comes away from the sides of the pan and forms a ball.
Remove from heat and transfer the dough to a mixing bowl. Let it cool slightly.
With an electric mixer, beat the dough for about 1 minute. Add the eggs while continuing to beat until the dough is smooth.
Beat in the shredded Havarti cheese until well blended; pipe or drop the small mounds of dough (about 1 1/2 teaspoons in size) onto the prepared baking sheet. Wet your finger and smooth any peaks on the mounds. Peaks can scorch in the hot oven.
Bake the puffs for 17 to 20 minutes, or until lightly browned. Remove from oven; cool.
Meanwhile, combine the finely chopped chicken with the remaining ingredients, adding extra mayonnaise, as needed, to moisten.
Split the cooled puffs horizontally with a sharp knife and then fill with about 1 tablespoon of the chicken salad mixture; replace the caps.
Refrigerate the little sandwich puffs until serving time.