I guess it depends what you're defining as paranormal, but this is one of my favorite Greek ghost stories which Pausanias includes when talking about Euthymus, an Olympic boxer:

Odysseus, so they say, in his wanderings after the capture of Troy was carried down by gales to various cities of Italy and Sicily, and among them he came with his ships to Temesa. Here one of his sailors got drunk and violated a maiden, for which offence he was stoned to death by the natives. Now Odysseus, it is said, cared nothing about his loss and sailed away. But the ghost of the stoned man never ceased killing without distinction the people of Temesa, attacking both old and young, until, when the inhabitants had resolved to flee from Italy for good, the Pythian priestess forbad them to leave Temesa, and ordered them to propitiate the Hero, setting him a sanctuary apart and building a temple, and to give him every year as wife the fairest maiden in Temesa. So they performed the commands of the god and suffered no more terrors from the ghost. But Euthymus happened to come to Temesa just at the time when the ghost was being propitiated in the usual way; learning what was going on he had a strong desire to enter the temple, and not only to enter it but also to look at the maiden. When he saw her he first felt pity and afterwards love for her. The girl swore to marry him if he saved her, and so Euthymus with his armour on awaited the onslaught of the ghost. He won the fight, and the Hero was driven out of the land and disappeared, sinking into the depth of the sea.