1. Heat 2 teaspoons oil in a soup pot over medium-high heat. Season the chicken with salt, add it to the pot, and cook, stirring, a few times, until just cooked through, about 5 minutes. Transfer to a dish and set aside.

2. Add the remaining 2 teaspoons olive oil to the pot, add the onion, celery, carrot, and thyme and cook, stirring, over medium-high heat until the vegetables are tender, about 5 minutes.

3. Add 5 cups of the broth and bring to a boil.

4. Add the orzo and let simmer until tender, about 8 minutes. Turn the heat down to low to keep the soup hot but not boiling.

5. Warm the remaining 1 cup broth in a small saucepan until it is hot but not boiling.

6. In a medium bowl, beat the eggs.

7. Gradually whisk the lemon juice into the eggs.

8. Then gradually add the hot broth to the egg-lemon mixture, whisking all the while.

9. Add the egg-lemon-broth mixture to the soup, stirring well until the soup is thickened. Do not let the soup come to a boil.

10. Add the cooked chicken to the soup. Season with salt and pepper and serve.