Cut the chicken crosswise into one-fourth-inch slices, then into one-half-inch-wide strips. Season with the salt and black pepper.
Heat the olive oil in a large, heavy pot over medium-high heat. Add the chicken and cook, stirring occasionally, until lightly browned, about 4 minutes. Add the onions and cook, stirring occasionally, until slightly soft, about 4 minutes. Add the mushrooms, garlic, and rice, and stir for 2 minutes, then add the chicken broth and bring to a boil. Reduce the heat to medium and stir constantly until the mixture is creamy and bubbly and the rice is tender, 15 to 18 minutes. Add the cream and butter and continue to stir for 2 minutes, then remove from the heat.
Add the cheese and green onions and stir until the cheese melts. Serve hot.
Makes 8 servings