Combine the chicken, white rice, celery, carrots, onions, garlic, salt, and pepper in a large pot. Add the chicken stock and bring to a boil over high heat. Once the soup is boiling, reduce the heat to keep the soup at a gentle simmer.

As the soup simmers, skim off any foam that collects on the surface with a spoon. Continue to simmer until the rice and vegetables are tender, about 25 minutes. Remove the soup from heat.

Remove the chicken and garlic cloves using a slotted spoon or tongs. Transfer the chicken breasts to a bowl and shred with two forks. Discard the bones. Return the shredded chicken to the pot. Smash the garlic cloves into a paste against a cutting board using a fork or the flat of your knife. Stir the paste back into the soup.

Stir the lemon juice into to the soup, and taste. The soup should taste rich, barely salty, and with just a hint of lemon. Add more salt or lemon juice as needed until it tastes good to you. Divide among bowls and sprinkle with some parsley for serving.