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 sliced carrots and celery to the pot, cooking for another 5 minutes until they begin to soften.
Pour in the chicken broth and bring the mixture to a boil. Once boiling, add the uncooked orzo pasta and cook according to package instructions, usually about 8-10 minutes.
Once the orzo is cooked, stir in the shredded chicken, lemon juice, and dried oregano. Season with salt and pepper to taste.
Remove the pot from heat and let it sit for a few minutes to allow the flavors to meld.
Serve hot, garnished with fresh parsley and lemon wedges on the side.