In a large saucepan set over medium-high heat, bring the broth to a boil. Add orzo and boil until just tender, about 7 minutes (1-2 minutes less than the package directions).
In a large bowl, beat the egg yolks until light in color. Slowly drizzle in 1 cup of the hot broth, whisking vigorously, until egg mixture is hot to the touch. Do this slowly to temper the egg yolks so they don’t cook and curdle.
Slowly add the egg mixture to the saucepan, reduce heat to medium, and cook, whisking occasionally, until thickened to the consistency of heavy cream, about 5 to 7 minutes.
Stir in lemon juice. Add chicken; cook for an additional few minutes until heated through. Season with salt and pepper to taste.