In the first decade of the fourth century AD, six men vied for the leadership of Rome, among them Maxentius (proclaimed emperor by the Roman Praetorian Guard) and Constantine the Great. In 312, Constantine advanced across the Alps toward an army commanded by Maxentius and challenged him at the Mulvian bridge over the Tiber. On the afternoon before the legendary battle, Constantine had a vision: a flaming cross outlined against the sun, emblazoned with the Greek words "En toutoi nika" (In this sign you shall conquer). Then, as he slept that night, a voice addressed him in a dream, commanding him to have his soldiers mark the chi rho (the monogram for Christ) upon their shields. Constantine obeyed, attacked Maxentius, and won.
[The words "In this sign you shall conquer" are often rendered in their Latin form as: "In hoc signo vinces."]
Sources
Little, Brown Book of Anecdotes