Bring a pot of salted water to a boil. Add wild rice, reduce heat to low, and simmer for 45 minutes until tender. Drain and set aside.
Heat olive oil in a large skillet over medium heat. Add onion and garlic and cook until softened, about 5 minutes. Add chicken and cook until lightly browned, about 5 minutes more. Add mushrooms, wine, broth, and thyme. Season with salt and pepper to taste. Bring to a boil, reduce heat to low, and simmer for 10 minutes.
In a separate saucepan, melt butter over medium heat. Add flour and stir to combine. Cook for 1 minute, then slowly add milk, stirring constantly. Cook until the sauce has thickened, about 5 minutes. Add the cheese and stir to combine.
In a large bowl, combine cooked wild rice, chicken mixture, and cheese sauce. Pour into a greased 9x13-inch baking dish. Bake for 30 minutes, or until the top is golden brown.
Interesting Facts
Wild rice is native to North America, and is a popular grain in many Native American cultures.
Casseroles are a great way to use up leftovers, so feel free to experiment with different ingredients.
This dish is a great make-ahead meal, as it can be prepared ahead of time and refrigerated until ready to bake.