Heat oil in a Dutch oven or stock pot over low-medium heat, and sauté onion until softened.
Add celery, carrot, and chicken, and cook, stirring occasionally until the chicken is cooked through.
Then, add the garlic, salt, pepper, rosemary, and parsley. Cook for another 30 seconds.
Next, add the orzo, lemon juice, and chicken broth. Stir to combine.
Cover and bring to a simmer.
Cook until the orzo is just tender, stirring occasionally. (This should take about 8 minutes once the soup begins to simmer).
Remove the lid and stir in the cream.
Then add in the spinach and stir until the spinach is wilted.
Serve immediately and enjoy!