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In a medium pot over medium heat, combine broth, water and chicken. Bring just to boiling, then stir in rice, reserving seasoning packet. Cover and remove from heat.
In a small bowl, combine salt, pepper and flour. In a medium saucepan over medium heat, melt butter. Add celery and carrots. Stir in contents of seasoning packet until mixture is bubbly. Reduce heat to low, then stir in flour mixture by tablespoons, to form a roux. Whisk in cream, a little at a time, until fully incorporated and smooth. Cook until thickened, 5 minutes.
Stir cream mixture into broth and rice. Cook over medium heat until heated through, 10 to 15 minutes.
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