Combine chicken broth, onion, celery, carrots, parsley, pepper, thyme, and bay leaf in a Dutch oven; bring to a boil.

Reduce heat to low; simmer until the onion and celery begin to soften. (10 to 15 minutes)

Stir chicken into the simmering broth; cook until the chicken is no longer pink in the middle. (5 to10 minutes)

Remove and discard bay leaf. Stir rice and lime juice into broth. Cook and stir just until rice is hot and grains separate. (1 minute)

Garnish with lime slices.