Trim leek, keeping root intact. Slice in half lengthwise, submerge in cold water, and rinse thoroughly to remove any dirt. Slice into 1/4" pieces.

Bring broth, water, and thyme to a low boil in a large saucepan. Add leek and mushrooms; reduce heat and simmer until leek is softened, about 5 minutes. Add chicken and brussel sprouts. Simmer until chicken is cooked through, about 6 minutes. Season with salt and pepper to taste, and serve hot.