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.