The Fall of the House of Usher

There is no literal prophecy per se, but Usher does predict his own end.

From the text:

"I shall perish," said he, "I must perish in this deplorable folly. Thus, thus, and not otherwise, shall I be lost. I dread the events of the future, not in themselves, but in their results. I shudder at the thought of any, even the most trivial, incident, which may operate upon this intolerable agitation of soul. I have, indeed, no abhorrence of danger, except in its absolute effect --in terror. In this unnerved-in this pitiable condition --I feel that the period will sooner or later arrive when I must abandon life and reason together, in some struggle with the grim phantasm, FEAR."

I learned, moreover, at intervals, and through broken and equivocal hints, another singular feature of his mental condition. He was enchained by certain superstitious impressions in regard to the dwelling which he tenanted, and whence, for many years, he had never ventured forth --in regard to an influence whose supposititious force was conveyed in terms too shadowy here to be re-stated --an influence which some peculiarities in the mere form and substance of his family mansion, had, by dint of long sufferance, he said, obtained over his spirit-an effect which the physique of the gray walls and turrets, and of the dim tarn into which they all looked down, had, at length, brought about upon the morale of his existence.