In a large pot over medium heat, melt butter and saute onions, carrots and celery until onions are translucent. Add apple and curry powder. Cook and stir until curry is fragrant, about two minutes. Add flour and stir to combine, cooking another two minutes.
Pour in chicken broth. Add chicken and rice. Bring up to a boil and turn heat down to medium-low, simmering about 20 minutes or until rice is cooked through, stirring occasionally to prevent rice from sticking to bottom of pan.
Season with salt and pepper to taste and pour in half-and-half. Ladle into bowls and serve while hot.