Place chicken in the Instant Pot.
Add leeks, carrots, barley, onion, bay leaf, and thyme to the Instant Pot.
Pour chicken broth over all ingredients.
Set manual cook time for 15 minutes. Let the pressure release naturally for 10 minutes, then release remaining pressure.
Remove the chicken breasts to a cutting board and shred. Return the shredded meat to the soup.
Serve topped with dried, diced prunes, if desired.