In a large stockpot, combine the rice, celery, carrots, chicken breasts, onion, garlic, salt, and black pepper. Pour in the chicken stock, ensuring all ingredients are well-submerged, and bring to a rolling boil over high heat.
Once it reaches a boil, reduce the heat to maintain a gentle, steady simmer. As it cooks, use a spoon to skim away any foam that rises to the top—this keeps the broth clear and clean-tasting.
Let the soup simmer uncovered for approximately 25 minutes, or until the rice and vegetables are tender and the chicken is fully cooked through. Remove the pot from the heat.
Using tongs or a slotted spoon, carefully lift out the chicken and garlic. Place the chicken in a bowl and shred it into bite-sized pieces with two forks, discarding the bones.
Mash the garlic into a smooth paste on a cutting board using the back of a knife or a fork. Return both the shredded chicken and mashed garlic to the pot, stirring gently to incorporate.
Add the freshly squeezed lemon juice and stir. Taste and adjust the seasoning with additional salt or lemon juice as desired. The final flavor should be deeply savory with a subtle citrusy brightness.
Ladle the soup into bowls and top with a scattering of fresh parsley.
Store any leftovers in the refrigerator for up to a week, or freeze for up to three months for a comforting, ready-made meal.