In a large pot, heat the olive oil over medium heat. Add the diced onion, carrots, and celery; sauté until softened, about 5-7 minutes.
Stir in the minced garlic and cook for another minute until fragrant.
Add the chicken breasts to the pot and pour in the chicken broth. Bring the mixture to a boil, then reduce the heat to low and let it simmer for 15-20 minutes, or until the chicken is cooked through.
Remove the chicken from the pot, shred it using two forks, and set it aside.
Once the chicken is removed, add the orzo pasta to the broth and cook according to package instructions (usually about 8-10 minutes).
In the last 2 minutes of cooking the orzo, stir in the fresh spinach, cooked shredded chicken, dill, lemon zest, and lemon juice.
Season the soup with salt and pepper to taste.
Remove the soup from heat and let it sit for a few minutes before serving.
Notes
Feel free to adjust the amount of dill and lemon to taste.