In a large saucepan over medium-high heat, bring the chicken broth to a boil.
Add the orzo and boil until just tender, about 7 minutes (about 1–2 minutes less than package directions).
Meanwhile, in a large bowl beat the egg yolks until they lighten in color.
Slowly drizzle 1 cup of the hot broth into the beaten yolks while whisking vigorously to temper them; the mixture should become warm but not scrambled.
Reduce the saucepan heat to medium. Gradually whisk the tempered egg mixture back into the saucepan.
Cook, stirring or whisking occasionally, until the soup thickens slightly to the consistency of heavy cream, about 5–7 minutes.
Stir in the Meyer lemon juice, then add the shredded chicken and cook 1–2 minutes until heated through.
Season to taste with kosher salt and black pepper, then serve warm.
