Pour broth into a five-quart pot and bring to a boil, covered, over high heat.
Add orzo and simmer briskly, still covered, until al dente (a minute shy of package directions).
Meanwhile, in a medium bowl, beat the eggs well with a fork. Beat in lemon juice and set aside.
When orzo is just cooked, ladle out about a cup of hot broth into a measuring cup with a spout.
Slowly pour hot broth into bowl with eggs and lemon juice, whisking constantly with a fork. This process tempers the eggs so they don’t scramble when you add them to the pot.
Stir chicken and spinach into soup pot and simmer for a minute or two until spinach is wilted.
Reduce heat until broth is no longer bubbling.
Stir egg mixture into soup and cook over low heat for a minute or two, until broth looks creamy and is slightly thickened.
Add salt and pepper to taste. Using lower-sodium broth, I recommend ½ teaspoon fine sea salt and ¼ teaspoon pepper.
