Cook brown rice with salt and one cup of water till three fourth done. Drain and keep aside. In a stockpot, combine the chicken with two cups of water. Bring to a boil, and then reduce heat to low.
Simmer for ten to fifteen minutes, or until chicken is cooked and tender. Remove chicken from the pot, and allow it to cool. Strain the broth from the pot, and reserve. When chicken is cool, shred and keep aside.
Heat oil in the same stockpot over medium heat and sauté celery and onion for five minutes. Add the mushrooms and cover. Cook for five minutes, stirring occasionally, until everything is tender.
Add the reserved broth and the partially cooked brown rice to the stockpot. Add white pepper powder, salt and simmer, uncovered, for fifteen minutes. Meanwhile, melt butter in a saucepan over medium heat. Stir in the flour until smooth.
Whisk in the milk and continue cooking until mixture is bubbly and thick. Add the broth mixture to the milk mixture, continuing to stir.
Mix in the shredded chicken and the white wine. Allow this to heat through for about fifteen minutes. Serve hot.