In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté for about 5 minutes until translucent. Stir in the minced garlic and cook for an additional minute until fragrant.
Add the diced carrots, celery, oregano, thyme, and red pepper flakes (if using) to the pot. Cook for about 5-7 minutes, stirring occasionally, until the vegetables begin to soften.
Pour in the chicken broth and bring the mixture to a boil. Once boiling, add the chicken breasts and reduce the heat to a simmer. Cook for 15-20 minutes, or until the chicken is cooked through.
Remove the chicken from the pot and shred it using two forks. Return the shredded chicken to the pot.
Stir in the uncooked orzo pasta and cook for an additional 8-10 minutes, or until the pasta is tender.
Add the chopped spinach and lemon juice to the soup. Season with salt and pepper to taste. Let it simmer for another 2-3 minutes until the spinach is wilted.
Serve hot, garnished with fresh parsley.