Passage 8.48.3
ἐνομίσθη δὲ ἐπὶ τοιῷδε· Θησέα ἀνακομιζόμενον ἐκ Κρήτης φασὶν ἐν Δήλῳ ἀγῶνα ποιήσασθαι τῷ Ἀπόλλωνι, στεφανοῦν δὲ αὐτὸν τοὺς νικῶντας τῷ φοίνικι. τοῦτο μὲν δὴ ἄρξαι λέγουσιν ἐντεῦθεν· τοῦ δὲ φοίνικος τοῦ ἐν Δήλῳ μνήμην ἐποιήσατο καὶ Ὅμηρος ἐν Ὀδυσσέως ἱκεσίᾳ πρὸς τὴν Ἀλκίνου θυγατέρα.
The origin of this custom is said to be as follows: they say that Theseus, when returning from Crete, celebrated athletic contests in Delos in honor of Apollo, and crowned the victors with palm-branches. From this event, they say, originated this practice. Homer too makes mention of the palm in Delos in the passage where Odysseus appeals as a suppliant to the daughter of Alcinous.