In a large pot, heat over medium heat and add oil. Season chicken with salt and pepper and add to pot. Cook to brown chicken on both sides. Add the minced garlic and stir together with the chicken for one minute.
Add the chicken broth, onion, celery, carrots, oregano, bay leaf, salt and pepper to the pot. Bring to a boil. Reduce heat to a simmer. Simmer covered for 20 minutes.
Remove the chicken and the bay leaf. Discard the bay leaf. Add the orzo to the pot and cook according to package instructions.
Meanwhile, shred the chicken. Add it back to the pot along with the chopped spinach the last minute when orzo is cooked.
Stir in the Mexican cheese. Once that is melted mix in the half and half. Makes 4 servings.