The Classical World Chess Championship 1995, known at the time as the PCA World Chess Championship 1995, was held from September 10, 1995, to October 16, 1995, on the 107th floor of the South Tower of the World Trade Center in New York City. Garry Kasparov, the defending champion, played Viswanathan Anand, the challenger, in a twenty-game match. Kasparov won the match after eighteen games with four wins, one loss, and thirteen draws.

The original World Trade Center (WTC) was a large complex of seven buildings in the Financial District of Lower Manhattan in New York City. It opened on April 4, 1973, and was destroyed during the September 11 attacks in 2001. At the time of their completion, the Twin Towers—the original 1 World Trade Center at 1,368 feet (417 m), and 2 World Trade Center at 1,362 feet (415.1 m)—were the tallest buildings in the world. Other buildings in the complex included the Marriott World Trade Center, 4 WTC, 5 WTC, 6 WTC, and 7 WTC. The complex contained 13,400,000 square feet (1,240,000 m2) of office space and, prior to its completion, was projected to accommodate an estimated 130,000 people.