Combine water, chicken, plantains, onion, cilantro, garlic, and salt in a large pot. Bring to a boil. Reduce heat to medium; cook until chicken is longer pink at the bone and the juices run clear, about 45 minutes. An instant-read thermometer inserted into the thickest part of the thigh, near the bone should read 165 degrees F (74 degrees C).
Remove the chicken and let cool. Add yuca, potatoes, and corn to the soup; cook over medium heat until yuca and potatoes are softened, about 30 minutes.
Discard chicken skin and bones. Place meat back into the soup; stir to combine.
