In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté for about 3-4 minutes until translucent.
Stir in the minced garlic, sliced carrots, and celery. Cook for an additional 5 minutes, stirring occasionally.
Pour in the chicken broth and bring the mixture to a boil.
Once boiling, add the uncooked orzo pasta and cook for about 8-10 minutes, or until the pasta is al dente.
Stir in the shredded chicken, lemon juice, and dried oregano. Season with salt and pepper to taste.
Simmer for another 5 minutes to heat through.
Serve hot, garnished with fresh parsley and lemon wedges on the side.