Cook orzo in boiling water about 5 minutes, until partially cooked through but not yet soft; drain and rinse with cold water until cooled.
Saute carrots and celery until they just begin to soften. Add garlic and cook 1 minute more. Add thyme, oregano, salt, and pepper; continue cooking another 30 seconds then add chicken broth.
Bring to a boil; partially cover pot, reduce heat, and cook about 10 minutes until vegetables are tender.
Stir orzo, lemon juice, lemon zest, and chicken into the broth and cook an additional 5 minutes, until orzo has softened. Add spinach and let wilt. Serve into bowls and garnish with lemon slices and Parmesan cheese.