Place the chicken breasts in the bottom of the slow cooker.
Add the chopped onion, minced garlic, diced tomatoes with their juice, chicken broth, dried oregano, dried basil, salt, and black pepper to the slow cooker. Stir gently to combine.
Cover and cook on LOW for 4 hours.
After 4 hours, remove the chicken breasts from the slow cooker and shred them using two forks.
Return the shredded chicken to the slow cooker.
Add the orzo pasta and olive oil to the slow cooker and stir well to combine.
Cover and cook on HIGH for 30 minutes, or until the orzo is tender and has absorbed most of the liquid.
Stir in the chopped baby spinach and grated Parmesan cheese until the spinach wilts and the cheese is well incorporated.
Taste and adjust seasoning with additional salt and pepper if desired.
Serve warm.