Remove all the meat from the rotisserie chicken and cut into bite sized pieces. Discard bones and skin, or save them for another use. Measure out 1 pound of the chicken to use in the soup (it will be about half of a large rotisserie chicken). Pack the remaining chicken in an airtight container or bag to refrigerate or freeze for another use.
Heat 1 Tablespoon olive oil in a dutch oven or large saucepan over medium-high heat. Add the chopped carrots, celery, onion, and 1/2 teaspoon kosher salt and cook, stirring occasionally until softened and just starting to brown. Stir in 1 clove garlic (minced), 1/2 teaspoon freshly ground black pepper, and 1/4 teaspoon dried thyme and cook until fragrant, about 1 minute.
Slowly pour in 6 cups chicken broth, scraping up any browned bits from the bottom of the pot. Bring to a boil. Add 2/3 cup barley and 1 bay leaf then reduce heat to medium. Simmer for 15-30 minutes until the barley is soft (see note)
Stir in the 1 pound of rotisserie chicken and cook until the chicken is cooked through. Add additional salt and/or pepper to taste if needed.
Notes
The cooking time will depend on the type of barley you used - use the cooking guidelines on the barley package to help you determine how long it needs to cook. Choose barley that cooks more quickly for a weeknight friendly, faster cooking soup.