Bring the broth and dill to a boil in a large saucepan. Add the orzo. Reduce the heat, and simmer 5 minutes or until the orzo is slightly tender. Remove from heat.
Place the eggs and juice in a blender; process until smooth. Remove 1 cup of broth from the pan with a ladle, making sure to leave out the orzo. With the blender on, slowly add the broth; process until smooth.
Add the carrot, salt, pepper and chicken to the pan. Bring to a simmer over medium-low heat, and cook 5 minutes or until the orzo is tender. Reduce the heat to low. Slowly stir in the egg mixture; cook 30 seconds, stirring constantly (do not boil).
Notes
Use cauliflower rice in place of the orzo if you want to cut down on carbs.
If you are preparing this soup as GLUTEN-FREE, use cauliflower rice instead of orzo, and just make sure that your chicken broth and roasted chicken do not contain any gluten.