Heat oil in a 5- to 6-quart Dutch oven over medium-high heat. Season the chicken with salt and pepper and add to the hot pan in a single layer. Cook until browned on the bottom, about 3 minutes, then stir until the chicken just loses its pink color, about 1 minute more.
Stir in the onion, carrots, celery, and a little more salt and pepper. Cook, stirring occasionally, until the onion is translucent, about 3 minutes. Add the broth and 4 cups water and bring to a boil.
Stir in pasta, return to a boil, and simmer until pasta is al dente, about 7 minutes. Stir in the peas and, if desired, dill and cook for 1 minute more.