While the chicken is simmering, heat the olive oil in a large pot over medium-high heat. Add the onion and cook for 5 minutes, stirring. Add the mushrooms, garlic, and carrots and cook for 8-10 minutes, stirring occasionally. Add the rice, additional 3 cups of water and the chicken to the pot, and season with salt and pepper. Bring to a boil and then lower the heat, and gently simmer for 1 hour, stirring occasionally. Taste for seasoning. Remove from the heat.