In a large pot, heat some oil over medium heat.
Add the onion, garlic, carrots, and celery. Cook until the vegetables are tender, about 5 minutes.
Add the chicken breasts, barley, chicken broth, bay leaf, thyme, salt, and pepper to the pot.
Bring the soup to a boil, then reduce the heat and simmer for 45-50 minutes, or until the chicken is cooked through and the barley is tender.
Remove the chicken from the pot and shred it. Return the shredded chicken to the pot and stir to combine.
Taste and adjust the seasoning if needed.
Serve the soup hot and enjoy!