Well, I believe the event would have to be a contemporary recorded instance of a solar eclipse. Early descriptions of solar eclipses, where we know the approximate time period they occurred and the location on Earth they were observed from and described, can be very accurately dated (even down to the hour and minutes local or GMT time they would have occurred in many cases) by using modern study of orbital mechanics to backtrack to the time period and place in question to accurately determine exactly when that solar eclipse must have happened.

There was a recorded description of a solar eclipse in China that is believed to have been the annular eclipse that we know (according to the NASA link above) took place there on October 22, 2137 B.C.E, though I know there is some debate about whether that was the actual eclipse being referenced in the specific ancient text. I believe the debate there has to do with the precise dating of the text itself that mentions the eclipse, as the text was dated to within a +/- 200-year time period, and there was more than one solar eclipse in that area of China over that time period.

Aside from that, the "Ugarit Eclipse" of May 3rd, 1375 B.C.E. I think is a likely candidate for the earliest known exact date of an historical event, as it was described in an ancient Mesopotamian clay tablet that was discovered in 1948 in modern Syria (amongst the excavated ruins of the ancient city of Ugarit). In that case, the translated quote from the tablet was that "On the day of the new moon, in the month of Hiyar, the Sun was put to shame, and went down in the daytime, with Mars in attendance."

If anyone knows of any other described historical event/incident that is older and can be precisely nailed down to an exact calendar date, please chime in, as it is an interesting topic I think!