(This is an incomplete answer since I don't know which eclipse specifically was predicted, nor how it compares to the rest of the world. But it is too long for a comment.)
Because of their cultural association of governmental legitimacy with astronomical/geophysical omens, ancient China was rather obsessed with predicting eclipses. Attempts to do so seemed to have begun in the Warring States era, but naturally were not very successful. Some breakthroughs were achieved in the Eastern Han when it was realised that the moon's motion is inconsistent.
By 20 B.C. the Chinese knew how eclipses were caused ... By 8 B.C. the Chinese could predict eclipses by using the 135 month period; and by A.D. 206 they could predict eclipses by analyzing the motion of the moon. By A.D. 390 they could predict how much of the moon would be in shadow.
- Thurston, Hugh, Early Astronomy, Springer, New York, 1994
These are referring to solar eclipses, as was made clear by the rest of the paragraph discussing ancient disputes over how the moon could block the sun's light. See also:
Astronomers were attached to the royal household as second tier functionaries ... One of the most important events to predict were eclipses. In the first century B.C. (the Han dynasty), an eclipse period of 135 months was recognized during which 23 eclipses were known. By the third century A.D., the astronomer Yang Wei was able to specify times of first contact for a solar eclipse.
Case Western Reserve University: Journey Through the Galaxy-
By about 20 BC, surviving documents show that Chinese astrologers understood what caused eclipses, and by 8 BC some predictions of total solar eclipse were made using the 135-month recurrence period. By AD 206 Chinese astrologers could predict solar eclipses by analyzing the Moon's motion.
- National Aeronautics and Space Administration: Eclipse Through Traditions and Cultures
It would therefore appear that, that by about the early third century, at least some eclipses were predicted.
Of course, these predictions were not very good, especially since the sun's movement had not been understood. That happened much later in the Tang Dynasty. The monk Yi Xing was able to produce better eclipse predictions based on his research. Another notable advancement in Chinese astronomy was achieved in the Yuan Dynasty, by the astronomers Wang Xun and Guo Shoujin.
This actual movement of the sun was fully understood by the famous astronomer Yi Xing (一行, 683-727 A.D), and he used the theory in his computations, for example the calculations for the time fo eclipses, in his Da Yan calendar (大衍歷, 729 A.D), getting accurate results in the process.
Guo and his co-workers were able to make more accurate astronomical calculations, which helped them to make better astronomical predictions, especially in the case of eclipses.
- Tiong, Ngsay, and and Helmer Aslaksen. "Calendars, Interpolation, Gnomons and Armillary Spheres in the Work of Guo Shoujin (1231–1314)."
Again, the eclipse predictions were still not perfect, especially over the course of centuries. However, a failed prediction was cause for commissioning a new calendar. Conversely, this meant that at least some of the predictions even in this early period were accurate, by chance or otherwise.
One major piece of evidence proposed by Xu in favour of the adoption of Western methods concerned eclipse predictions ... [E]clipse prediction was the touchstone. In 1610, when it was first proposed to employ Jesuits for astronomical reform, the miscalculation of a solar eclipse was used to make the case for the necessity of this reform.
- Jami, Catherine, et al, eds. Statecraft and Intellectual Renewal in Late Ming China: the Cross-Cultural Synthesis of Xu Guangqi (1562-1633). Vol. 50. Brill, 2001.
At this juncture the then-extant Chinese calendars were failing in their predicative powers. The Court held a competition (to predict an eclipse) between the Chinese court astronomers and the Westerners, which resulted in a resounding victory for European astronomy.