Bring water to a boil in a saucepan with a cover. Add rice (and additional salt and pepper, to taste), cover, and lower temperature to a simmer. Cook for 40 minutes, stirring periodically.
While the rice is cooking, prepare the vegetables. Add olive oil to a soup kettle and heat over medium heat.
Once oil is hot, add onions, celery, carrots and garlic. Cook for 8-10 minutes, until they are beginning to soften. Add mushrooms and cook an additional 4-5 minutes.
Remove vegetables from the kettle. Lower the temperature slightly. Add butter and allow to melt.
Once melted, add flour, creating a roux. Cook for 2-3 minutes, stirring constantly.
Slowly add milk, about ⅓ cup at a time, stirring the whole time, allowing the mixture to just begin to boil before you add more. Add the chicken stock in a similar nature. Add thyme, salt, and pepper.
Stir in the rice from the saucepan, including any remaining liquid. Reincorporate the vegetables and stir in the chicken. Allow to cook an additional 10-20 minutes.