Heat 1 tablespoon of olive oil in heavy pot over medium high heat. Season chicken generously with salt and pepper. Brown chicken, about 4-5 minutes per side. Remove chicken from pot and set aside.
Add remaining olive oil to pot. Add onions, carrots, and celery and cook until softened and just start to brown, about 4-5 minutes. Add garlic and cook for 1 minute more.
Add chicken broth, salt, pepper, thyme, and browned chicken to pot (along with any juices from the browned chicken). Zest the lemon and add zest to the pot.
Bring to a boil and then add farro. Simmer for 20 minutes until farro is tender.
Chicken may be cooked through before 20 minutes are up, depending on the size or your breasts or thighs. Check with an instant read thermometer (chicken is done at 165°), or by cutting chicken open to see if it's cooked through. When chicken is done, remove from pot and let cool slightly, then shred.
When farro is tender, add shredded chicken back to pot. Add juice from half of the lemon. Taste soup, and if desired, add more lemon juice and/or salt. Serve hot.
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