Kithairon, or Cithaeron, is not a who but a what. Kithairon is the western area of a mountain range in Greece. It serves as the border between Athens and Thebes. And it is on the side of that mountain that Oedipus, as a baby, was abandoned to die.
It goes like this:
We learn in the play, as Oedipus himself learns, that Oedipus' father, King Laius, and mother, Queen Jocasta, were unable to have children. King Laius sends for an oracle to see if he can help the couple with this problem. The oracle tells Laius that if he has a son the son will grow up and kill his father and marry his mother. And they do have a son. Horrified by the prophesy, Laius has a pin put through the baby's ankles, his feet are bound together, and the baby is given to a messenger. The messenger is ordered to abandon the baby, and he does so on the side of a mountain, Mount Kithairon. We learn, as does Oedipus, that a shepherd found the bound baby on the mountainside and saves him. The rest, as they say, is history... and the prophesy is fulfilled.
Near the end of the play, Oedipus, who has finally learned the truth of his existence, says he will go back to where he was, so long ago, left to die:
But for myself, O never let my Thebes,
The city of my sires, be doomed to bear
The burden of my presence while I live.
No, let me be a dweller on the hills,
On yonder mount Cithaeron, famed as mine,
My tomb predestined for me by my sire
And mother, while they lived, that I may die
Slain as they sought to slay me, when alive.