In a medium saucepan on medium heat, simmer chicken in chicken broth until cooked through, about 20 minutes. Remove chicken and dice it into bite-size pieces. Transfer remaining chicken broth into a medium bowl and add enough water to reach 2 cups. Set aside.
Melt butter in saucepan over medium heat. Add onion and celery, saute until glassy and transparent. Add flour to make a roux. Cook while stirring for 1 minute, but do not allow to brown. Gradually add reserved chicken broth, stirring constantly. Add chicken, corn, cannellini beans, thyme and pepper. Taste before adding salt. Simmer on low heat for 10 minutes.
Spoon half a cup of rice into four soup bowls. Top with stew. Sprinkle with cheese and parsley if desired before serving.