Heat olive oil in a large pot over medium high heat. Add garlic, carrots, celery, and onion. Cook until tender, 5-7 minutes.
Add rosemary, bay leaves, chicken stock, and chicken. Bring to a boil then add the orzo pasta. Reduce heat and simmer until the pasta is cooked, about 9 minutes.
Stir in the spinach. Season with salt and pepper to taste.