The break between the Eastern (Orthodox) and Western (Catholic) churches, often referred to as the Great Schism, is generally dated to
1054 AD.
However, it's important to understand that the schism wasn't a single, clean event. It was a gradual process built upon centuries of growing theological, political, and cultural differences. While 1054 marks a key moment of formal excommunications between the Pope's legate and the Patriarch of Constantinople, the complete reconciliation of the churches has not been achieved to this day.
Therefore, the answer is 1054, but with the understanding that it was a culmination of events and not a sudden, isolated incident.