This recipe can be made low carb by eliminating the rice.
Bring the first 5 ingredients to a simmer. Add chicken breasts and simmer until just barely cooked, about 10 minutes. Remove and cool. Cut into thin strips.
Strain the soup. Return the chicken. Use or toss the carrots and onions, as you prefer.
Whisk the egg with a splash of lemon juice, the rest of the juice can go into the broth, according to taste. If you whisk in less juice, it’s more like egg drop. If you whisk in more juice, it’s creamy.
For a creamy soup, very slowly mix some hot broth into the egg, stirring, and then add it to the pot. If you want it more like egg drop, pour a steady stream of egg into the soup pot, stirring.
Salt to taste and serve the soup with a ball of rice for those who want it. Garnish with parsley and pepper.