Laudator Temporis Acti

There is no evidence that a torch relay was ever part of the ancient Olympic games. Carl Diem (1882-1962) first introduced it as part of the modern Olympics in the 1936 games in Berlin.

However, the ancient Greeks were fond of both simple torch races and torch relay races. Pausanias (1.30.2, tr. W.H.S. Jones) describes a torch race that was not a relay race:

In the Academy is an altar to Prometheus, and from it they run to the city [Athens] carrying burning torches. The contest is while running to keep the torch still alight; if the torch of the first runner goes out, he has no longer any claim to victory, but the second runner has. If his torch also goes out, then the third man is victor. If all the torches go out, no one is left to be winner.

Plutarch (Life of Solon 1.4, tr. Bernadotte Perrin) gives a further detail about this race:

And it is said that Peisistratus also had a boy lover, Charmus, and that he dedicated the statue of Love [Eros] in the Academy, where the runners in the sacred torch race light their torches.

Herodotus (8.98.2, tr. Aubrey de Selincourt) compares horse-riding Persian mail couriers to Greek torch racers:

The first, at the end of his stage, passes the dispatch to the second, the second to the third, and so on along the line, as in the Greek torch-race [lampadephorie] which is held in honour of Hephaestus.

Obviously this was a torch relay race.

Herodotus also (6.105.1-3) mentions the origin of torch races in honor of the god Pan:

Before they left the city, the Athenian generals sent off a message to Sparta. The messenger was an Athenian named Pheidippides, a trained runner still in the practice of his profession. According to the account he gave the Athenians on his return, Pheidippides met the god Pan on Mount Parthenium, above Tegea. Pan, he said, called him by name and told him to ask the Athenians why they paid him no attention, in spite of his friendliness towards them and the fact that he had been useful to them in the past, and would be so again in the future. The Athenians believed Pheidippides' story, and when their affairs were once more in a prosperous state, they built a shrine to Pan under the Acropolis, and from the time his message was received they have held an annual ceremony, with a torch-race and sacrifices, to court his protection.

At the beginning of the Republic (1.328a, tr. Paul Shorey), Plato describes a torch relay race in honor of the Thracian goddess Bendis, with an added twist. The racers were on horseback:

Do you mean to say, interposed Adimantus, that you haven't heard that there is to be a torchlight race this evening on horseback in honor of the goddess?

On horseback? said I. That is a new idea. Will they carry torches and pass them along to one another as they race with the horses, or how do you mean?

That's the way of it, said Polemarchus, and besides, there is to be a night festival which will be worth seeing.

Plato also uses the metaphor of a torch relay race in Laws 6.776b (tr. A.E. Taylor):

They will pay visits to the old home and receive visits from it, beget children and bring them up, and thus hand the torch of life on from one generation to another and perpetuate that service of God which our laws demand.

Lucretius imitates the same metaphor when he writes (2.79) "like runners they pass on the torch of life" (quasi cursores vitai lampada tradunt).

According to Aristophanes, Frogs 1089-1098 (tr. Gilbert Murray), the Athenians also ran torch races in honor of Athena:

Not a doubt of it! Why, I laughed fit to cry
At the Panathenaea, a man to espy,
  Pale, flabby, and fat,
  And bent double at that,
Puffing feebly behind, with a tear in his eye;

Till there in their place, with cord and with brace,
Were the Potters assembled to quicken his pace;
  And down they came, whack!
  On sides, belly, and back,
Till he blew out his torch and just fled from the race!

Aristotle says (Athenian Constitution 57.1) that all of the torch races at Athens were under control of the archon basileus, the king archon. A red-figure krater of 430 B.C. (Harvard University Art Museums 1960.344) shows torch race runners plus the archon basileus.

The modern Olympic torch relay is not a race, but all of the ancient Greek examples just cited were. The agon, or contest, was a central feature of ancient Greek life. Nietzsche's friend Jacob Burckhardt emphasized this in his lectures on Greek cultural history -- see the selections from these lectures published as The Greeks and Greek Civilization, tr. Sheila Stern (New York: St. Martin's Press, 1998), pp. 160-213 (The Agonal Age).