Start the soup: Set a large soup pot over medium heat.

Add the olive oil to the pot and let it warm for about 30 seconds.

Add the chopped onion, diced carrots, and sliced celery to the pot.

Stir in the salt and black pepper, then cook the vegetables for 6 to 8 minutes, stirring every so often, until the onion looks soft and the carrots begin to lose their raw edge.

Pour the chicken broth into the pot and raise the heat to high.

Bring the broth to a full boil.

Add the rinsed rice to the boiling broth and stir once so it does not stick to the bottom of the pot.

Lower the heat to medium-low and simmer for 12 to 15 minutes, until the rice is tender and the carrots are easy to cut with the side of a spoon.

Put the shredded chicken into the pot and stir it into the soup.

Cook the soup for 2 to 3 minutes more, until the chicken is hot all the way through.

Warm the eggs and lemon: Crack the eggs into a medium bowl and whisk until the yolks and whites are fully mixed.

Whisk the lemon juice into the eggs until smooth.