Heat the oil over medium-high heat in a Dutch oven or stockpot
Cook the chicken over medium-high heat, about 3 minutes per side. You'll want the chicken to develop a nice brown sear on the outside, but it won't be cooked all the way through.
Add the chopped carrots, celery and leeks to the pot. Turn the heat down to "medium" and put the lid on. Let the veggies sit and steam for about 3 to 5 minutes.
Add the chicken stock, barley, prunes and bay leaf to the pot. Turn the heat up to "high" and bring the soup to a boil.
Once the soup begins to boil, turn the heat down to "low" and allow the soup to simmer, lid on, for about 30 minutes.
Soup is done when the chicken is cooked all the way through and the barley is tender.
Remove the fully-cooked chicken from the pot and transfer it to a plate.
Shred the chicken with 2 forks, and stir the shredded chicken back into the soup.