Combine broth and diced chicken in a large pot.
Bring to a boil over medium heat.
Add rice, but not seasoning packet. Cover and remove from heat.
Melt butter in a medium pan over medium heat.
Add carrots, celery and onion. Cook for 7 minutes.
Add contents of seasoning packet and continue cooking for 5 minutes until carrots are softened.
In a small bowl, whisk together flour and pepper.
Sprinkle flour mixture over vegetables while stirring constantly until incorporated.
Cook another 5 minutes.
Gradually stir in half and half until incorporated.
Cook about 5 minutes until thickened.
Add vegetable mixture to chicken and rice mixture.
Cook over medium heat 15-20 minutes until heated through and rice is done.