Heat a large, lidded nonstick skillet over medium-high heat. Add chicken, skin-side down, and cook until browned, 4 to 5 minutes. Add 4 cups water, cover and reduce heat to a simmer. Poach 20 minutes, or until cooked through. Remove chicken from liquid (save liquid) and let cool. When cool enough to handle, remove and discard skin and bones and cut chicken into bite-size pieces.
Heat oil in a large pot over medium heat. Add carrots, celery and leek. Cook 5 minutes or until softened. Sprinkle with flour, salt and pepper. Cook 3 minutes, stirring. Add broth and 2 cups of the poaching liquid. Bring to a simmer; cook 5 minutes. Stir in chicken.
In medium bowl, combine biscuit mix, milk and dill. Drop by tablespoonfuls into simmering liquid. Cover pot tightly; cook 10 minutes. Uncover and gently stir in peas and chopped dill.