This legendary 2nd-century Christian martyr's story is told in Chapter 14. Also known as Eustatius or Eustachio, he reportedly began as a Roman soldier named Placidus, who converted to Christianity after seeing a vision of Christ between the antlers of a stag. He was then tested by the loss of his family in a series of tragic misadventures (including losing his sons to a wolf and a lion while trying to cross a river), but they were restored to him and he achieved honor in the Roman army before being martyred for his faith. He is a patron saint of hunters*.
However, the entire story may be apocryphal, and Eustace is not recognized by the Anglican nor the Catholic Church. There are many unrelated saints of the same name: Eustace of Vilna, Eustathius Bishop of Antioch, Eustace of Luxeuil, etc.
The vision of the stag is commonly thought to be a borrowing from pre-Christian mythology. In Celtic myth, a white stag appears when the hero is called to a quest, or has entered a magical or forbidden realm. In the Welsh Mabinogion, the prince Pwyll accidentally trespasses on a hunt led by Arawn, lord of the underworld, who is hunting a white stag; Arawn's hunting hounds also pursue the souls of the damned.
Hungarian legend includes a mystical stag, son of a horned doe who carries the sun between her horns. In an origin myth of the Huns and Magyars, the Legend of the Hind, a king goes on a hunt for this doe accompanied by his twin sons, who are separated from their father along the way. [EB]
* (The stag-and-cross logo on Jägermeister liqueur [Jäger means hunter] is not actually a reference to Eustace, but to Saint Hubert, whose conversion story is identical and was probably borrowed from the earlier legend.)