A paean (/ˈpiːən/ ^ⓘ) is a song or lyric poem expressing triumph or thanksgiving. In classical antiquity, it is usually performed by a chorus, but some examples seem intended for an individual voice (monody). It comes from the Greek παιάν (also παιήων or παιών), "song of triumph, any solemn song or chant". "Paeon" was also the name of a divine physician and an epithet ("byname") of Apollo.

The basis of the word παιάν is *παιάϝων." Its ultimate etymology is unclear. R. S. P. Beekes has suggested the meaning "who heals illnesses through magic", from *παῖϝα/*παϝία "blow", related to παίω "beat" (from Proto-Indo-European *ph₂u-ie/o-) or παύω "withhold" (of uncertain etymology). He alternatively suggested that paian "may well be Pre-Greek".

In Homer, Paeon was the Greek physician of the gods. In Iliad V he heals the wounded Ares and Hades with his herbal lore. In time Paeon (or Paean) became an epithet ("byname") of Apollo as a god capable of bringing disease and propitiated as a god of healing. Hesiod identifies Paeon as a separate god, and in later poetry Paeon is invoked independently as a health god. Later, Paean becomes a byname of Asclepius, another healer-god.

The earliest appearances of a paean or hymn of thanksgiving also appear in the Iliad. After the prayer to avert evil from the Achaeans, a paean is sung. In an almost identical line (X.391) that suggests a formulaic expression, Achilles tells the Myrmidons to sing the paean after the death of Hector.

Previously, L. R. Farnell had referred to the ancient association between the healing craft and the singing of spells, but found it impossible to decide which was the original sense. At all events the meaning of "healer" gradually gave place to that of "hymn", from the phrase "Ἰὴ Παιάν" or "Ἰὼ Παιάν".

Such songs were originally addressed to Apollo, and afterwards to other gods, like Dionysus, Helios, and Asclepius. About the 4th century the paean became merely a formula of adulation; its object was either to implore protection against disease and misfortune, or to offer thanks after such protection had been rendered. Its connection with Apollo as the slayer of the Python led to its association with battle and victory; hence it became the custom for a paean to be sung by an army on the march and before entering into battle, when a fleet left the harbour, and also after a victory had been won.

The Greek poet Aeschylus who took part in the Battle of Salamis, commented on the power of the paean over enemies (in this case the Persians):

All the barbarians felt fear because they had been deprived of what they expected. The Greeks were singing the stately paean at that time not for flight, but because they were hastening into battle and were stout of heart.