This list of mythical creatures that begin with this letter and I am constantly gathering information from each continent, and is continually being updated.
Cu Bird (Mexican)
The Cu bird is a bird from a Mexican folktale that is unhappy with its looks. According to the legend, the other birds agreed to the barn owl's proposal to give the Cu bird one feather each and in return asked it to become the messenger of the bird council. But the bird soon started neglecting its task because instead it spent time admiring its plumage.
Another version is a ballad. The Cu bird has no feathers, so the barn owl and the hoot owl (tecolote) organize all the birds to donate a feather each to it; the hoot owl guarantees that the Cu bird will not be a "traitor". However, once the Cu bird is dressed, it flies to better lands, and the other birds blame the hoot owl. This is why the latter calls at night to the Cu bird, Ticu-ticu, and why it cannot see during the day.