Pour broth into a large stockpot and bring to a boil over medium.
Peel potatoes and chop into 1/2 inch cubes; add to boiling stock. Return to boil and then simmer for 7-8 minutes or until potatoes are just tender. (Avoid overcooking so potatoes won't break apart.)
Add kale and mushrooms and continue to simmer for 5 minutes.
Slice chicken and toss into stock. Season with pepper. Simmer until chicken has cooked through, and is no longer pink.