In the Myth of Prometheus the Titan is sentenced to be chained to a rock for all eternity. An avian of some sort is then mentioned as coming every day to peck out his liver, but leave him alive, only to heal the liver overnight and repeat the process each following day.
The type of avian changes depending on which version of the myth you are consulting. Since mythology was origianlly an oral tradition, the telling changed over time and location and the local disposition toward the subject of the myths. Therefore, we find several different flying creatures mentioned in the various tellings of the Prometheus myth.
Most common animals include the eagle, since that was the favored bird of Zeus, a vulture as the eater of carrion and a common pest for the farming communities of the Caucasus Mountains, and a hawk as another fierce carnivore common to the region. There is also the mention of a griffon, a fantasy monster combining lion and eagle as two symbols of regal power as extensions of the vengeance of the Ruler of Mount Olympus.
One interesting factoid which surfaced during research on the mythology of Prometheus is that it was customary for remote villages on the heights of the Caucasus mountains to go on an annual hunt of Griffon Vultures (Gyps fulvus.) with flaming arrows, in honor of Prometheus in relatively recent times (circa 1950s). More likely the myth was utilized as an excuse to hunt the birds, which were widely regarded as pests, but which now are diminishing seriously in Europe as a result of the loss of open pastures in which to 'hunt' for dead animals.
The Myth of Prometheus
Greek and Roman Mythology