In a large pot or Dutch oven, heat the olive oil over medium heat.
Add the chopped onion, carrots, and celery. Sauté for about 5-7 minutes until the vegetables are softened.
Stir in the minced garlic and cook for an additional minute until fragrant.
Add the boneless chicken breasts to the pot, followed by the chicken broth, bay leaf, dried thyme, salt, and pepper.
Bring the mixture to a boil, then reduce the heat to low and cover. Let it simmer for about 30 minutes, or until the chicken is cooked through and tender.
Remove the chicken from the pot and shred it using two forks. Discard the bay leaf.
Return the shredded chicken to the pot, stir in the frozen peas, and cook for another 5 minutes until heated through.
Taste and adjust seasoning if needed. Serve hot, garnished with fresh parsley.