In a large pot, heat the olive oil over medium heat. Add the chicken breasts or thighs and season with salt and pepper. Sear the chicken for about 5-7 minutes on each side, or until golden brown. Remove the chicken from the pot and set it aside.
In the same pot, add the minced garlic and sauté for about 1 minute until fragrant. Be careful not to let it burn.
Pour in the chicken broth and bring it to a gentle simmer. Add the dried oregano, dried thyme, and the seared chicken back into the pot.
Cover and let the chicken simmer for 15-20 minutes, or until cooked through. Once done, remove the chicken and shred it using two forks.
Return the shredded chicken to the pot and stir in the uncooked orzo pasta. Cook for an additional 8-10 minutes, or until the orzo is tender.
Stir in the fresh spinach, lemon juice, and lemon zest. Cook for another 2-3 minutes until the spinach wilts.
Taste and adjust the seasoning with more salt, pepper, or lemon juice as desired.
Serve the soup hot, garnished with fresh dill or parsley.