Heat oil in a large heavy pot over medium heat. Add leek and celery and cook, stirring often, until vegetables are soft, 5-8 minutes. Add chicken and broth
season with salt and pepper. Bring to a boil, cover, reduce heat, and simmer until chicken is cooked through, 15-20 minutes. Transfer chicken to a plate. Let cool, then shred chicken into bite-sized pieces.
Meanwhile, return broth to a boil. Once boiling, pour in the RightRice, remove the pot from heat, and let sit for 10 minutes.
RightRice will expand and cook on its own in the broth. When the timer goes off, stir in chicken and dill. Serve with lemon halves for squeezing over.