W/some Googling, I'll say ~ 300 BC:
Ancient Macedon
In the time of Alexander the Great the custom of smooth shaving was introduced.[18] Reportedly, Alexander ordered his soldiers to be clean shaven, fearing that their beards would serve as handles for their enemies to grab and to hold the soldier as he was killed. The practice of shaving spread from the Macedonians, whose kings are represented on coins, etc. with smooth faces, throughout the whole known world of the Macedonian Empire. Laws were passed against it, without effect, at Rhodes and Byzantium; and even Aristotle conformed to the new custom,[19] unlike the other philosophers, who retained the beard as a badge of their profession. A man with a beard after the Macedonian period implied a philosopher,[20] and there are many allusions to this custom of the later philosophers in such proverbs as: "The beard does not make the sage."[21]
[edit] Ancient Rome
Shaving seems to have not been known to the Romans during their early history (under the Kings of Rome and the early Republic). Pliny tells us that P. Ticinius was the first who brought a barber to Rome, which was in the 454th year from the founding of the city (that is, around 299 BC). Scipio Africanus was apparently the first among the Romans who shaved his beard. However, after that point, shaving seems to have caught on very quickly, and soon almost all Roman men were clean-shaven; being clean-shaven became a sign of being Roman and not Greek.