327 BC

By place

Macedonian Empire

• Alexander the Great invades northern India. Recrossing the Hindu Kush, Alexander divides his forces. Half the army with the baggage under Hephaestion and Perdiccas, both cavalry commanders, are sent through the Khyber Pass, while Alexander leads the rest, together with his siege train, through the hills to the north. His advance through Swat and Gandhara is marked by the storming of the almost impregnable pinnacle of Aornos, a few miles west of the Indus.
• The relations between Alexander and Aristotle are embittered by the execution of Aristotle's nephew, the historian Callisthenes of Olynthus, who is charged with treason. Callisthenes has been accompanying Alexander to write a chronicle of the campaign.

Roman Republic

• The Samnite army captures Neapolis (present-day Naples). The Romans, who are meanwhile moving south while the Samnites are occupied with Tarentum, take the opportunity to recover Neapolis and, after a long siege, evict the Samnite garrison from the city and make it an ally of Rome.

• Heracles, illegitimate son of Alexander the Great by his mistress Barsine, daughter of Satrap Artabazus of Phrygia and later claimant to the throne of Macedon (d. 309 BC)
• Moggaliputta-Tissa, Indian Buddhist monk, scholar and philosopher (approximate date)

• Callisthenes of Olynthus, Greek historian, great nephew and pupil of Aristotle (b. c. 360 BC)