In a large pot, heat olive oil over medium heat. Add the diced onion, carrots, and celery. Sauté for about 5-7 minutes until the vegetables soften.
Add the minced garlic and cook for another minute until fragrant.
Push the vegetables to the sides of the pot and add the chicken thighs in the center. Season with salt and pepper. Sear the chicken for about 5 minutes on each side until browned.
Pour in the chicken broth and bring the mixture to a boil. Reduce to a simmer and cover the pot. Cook for 20 minutes, or until the chicken is cooked through.
Remove the chicken from the pot and shred it using two forks. Return the shredded chicken to the pot.
Stir in the orzo pasta and cook for an additional 8-10 minutes, or until the pasta is tender.
Lower the heat and stir in the heavy cream, lemon zest, and lemon juice. Allow it to simmer gently for 3-5 minutes until everything is heated through.
Add the fresh spinach and stir until just wilted. Adjust seasoning with more salt and pepper if needed.