Heat the olive oil in a large Dutch oven or stockpot over medium heat.
Add the onion, carrots, and celery. Sauté for 6 to 8 minutes until the vegetables have softened.
Add the minced garlic and cook for 60 seconds until fragrant.
Place the whole chicken breasts, rinsed farro, chicken broth, thyme, oregano, salt, and pepper into the pot.
Bring the mixture to a boil, then immediately reduce the heat to a low simmer.
Cover and cook for 25 to 30 minutes, or until the farro is tender and the chicken reaches an internal temperature of 165°F (74°C).
Remove the chicken breasts from the pot and transfer to a cutting board. Shred the meat using two forks.
Return the shredded chicken to the pot and stir in the spinach and lemon juice.
Simmer for an additional 2 minutes until the greens are wilted. Taste and adjust seasoning with additional salt or pepper as needed.