Heat the olive oil in a large pot over medium heat. Add the onion, carrots, and celery and cook until the vegetables soften, about 5 minutes.
Stir in the garlic and oregano and cook for 1 minute until fragrant.
Pour in the chicken broth and bring the mixture to a boil.
Add the orzo and cook until tender, about 8 to 10 minutes.
Stir in the shredded rotisserie chicken and lemon juice. Season with salt and pepper to taste.
Ladle into bowls and top each serving with fresh dill.