Heat the chicken stock over medium-high heat in a heavy, medium saucepan to 180° or until tiny bubbles form around the edge. Do not boil.
Combine the eggs, lemon zest, lemon juice, and salt in a medium bowl. Whisk until the eggs are frothy and lighter in color. (Alternatively, you can use a blender.)
Ladle about a cup of the hot chicken stock into the egg mixture 1/4 cup at a time, while stirring constantly (but not too vigorously) with a whisk.
Lower the heat on the remaining chicken stock to as low as possible. Wait for 2 minutes, and then add the egg, lemon, and stock mixture back to the pot, stirring to combine.
Warm the sauce gently, until it reaches 180° and coats a spoon. Turn off the heat.
Whisk in the olive oil to finish.