He gives us the story of his conversion in Book I of the De Trinitate. He spent an extended period reflecting on the meaning of life; on the basis of such reflection he rejected the view that life should be spent seeking material satisfaction; rather, a life of virtue was the only life that was fitting for a human being. But when he looked at the philosophers around him, he had difficulty finding any philosophy that rose above the mere animal minimum -- none of them really called human beings to the best and the highest. The kind of moral philosophy that human understanding calls out for, he thought, could not rest in anything other than something divine. But this, too, was a problem. When he looked around at the philosophers of the day, he found a wide variety of views, and, like many pagans of Neoplatonist bent in this age, he came to the conclusion that bare polytheism was itself not sufficient: the divine must have both eternity and power over all, and these were not communicable or divisible.
So far many other pagan Neoplatonists had gone, and not gone any further. But a happenstance changed Hilary's life forever:
While my mind was dwelling on these and on many like thoughts, I chanced upon the books which, according to the tradition of the Hebrew faith, were written by Moses and the prophets, and found in these words spoken by God the Creator testifying of Himself 'I Am that I Am, and again, He that is has sent me unto you.' I confess that I was amazed to find in them an indication concerning God so exact that it expressed in the terms best adapted to human understanding an unattainable insight into the mystery of the Divine nature. For no property of God which the mind can grasp is more characteristic of Him than existence, since existence, in the absolute sense, cannot be predicated of that which shall come to an end, or of that which has had a beginning, and He who now joins continuity of being with the possession of perfect felicity could not in the past, nor can in the future, be non-existent; for whatsoever is Divine can neither be originated nor destroyed. Wherefore, since God's eternity is inseparable from Himself, it was worthy of Him to reveal this one thing, that He is, as the assurance of His absolute eternity.
And reading further only confirmed the impression: here at last was the divine he had been seeking.