Gently simmer chicken and broth in large pot 18 to 22 minutes until chicken 165°F. Transfer chicken to plate.
Add rice, salt, and white pepper; simmer 15 to 18 minutes until tender. Meanwhile, shred chicken.
Whisk eggs and lemon juice smooth in heatproof bowl. Slowly whisk in 2 cups hot broth, adding first cup a few tablespoons at a time to gradually warm eggs.
Lower heat; add tempered eggs and chicken. Stir gently 2 to 4 minutes until silky and 160 to 165°F; do not boil.
Immediately remove from heat; serve while broth smooth and pale.