Asclepius

Asclepius is the Greek god of healing. Historically, he may have been a hero who, over time, was elevated to the level of a deity. By legend, his father, Apollo, sent him to the Centaur Chiron to be instructed in the art of medicine. He proved to be a most advanced pupil. Not only was he able to cure the ill but he could restore life to the dead as well. Fearing that his restorative powers would upset the natural order, Zeus is purported to have eventually struck him down with a lightening bolt. Upon his death, Asceplius was transformed into a constellation.

Tradition suggests that Socrates believes he is being "cured" of the pains and sorrows of this world's injustices by passing on to the Underworld. In this sense, he is being healed of an illness and, thus, the reference to sacrificing a cock to Asclepius.