Lewis and Short indicates that "chorāgus" is from Greek χορηγός (Doric χορᾱγός), which LSJ says is a compound of χορός and ἡγέομαι. The entries for choragus in the Oxford English Dictionary and a number of other English dictionaries say instead that the second element is from ἄγω, which seems to contradict the LSJ entry.
I wondered whether the long vowel that is supposed to be in the Latin word would be consistent with the derivation from ἄγω, since I thought that verb usually had a short vowel. However, when I checked the LSJ entries for ἄγω and the noun ἀγός, they seemed to indicate that the alpha is sometimes found long.
Is there a chance that the Oxford English Dictionary's etymology is correct after all, or is it just a mistake?