In a large pot, add the olive oil and heat over medium heat. Add the onion, garlic, carrots, celery, seasonings and bay leaves. Cook for 10 minutes, or until the vegetables are softened, and stir frequently so the veggies don't burn.
Pour in chicken broth, and water (I like to add a couple of chicken bouillon cubes for added flavor) and bring to a boil.
Add the rice and the chicken, cook on medium-low until the rice is tender, about 25-30 minutes.
The rice will soak up a lot of the broth as it starts to cool. If so, add more broth/stock or water and add more bouillon cubes for flavor.