Add 1 cup of the broth to a blender with the beans. Blend until smooth. Add to the stockpot with the onion, carrots, and celery.
Add the remaining 5 cups of broth to the pot, along with the rice. Stir and cover. Bring to a boil and then let simmer, covered, for about 25-30 minutes, until the rice has cooked.
Remove the lid and add the chicken, lemon juice, fresh dill, salt, and pepper. Stir to combine. Cook for another 5 minutes over medium heat, until everything is well combined and warmed through.