Carlos "White Feather" Hathcock is the man you are talking about, this is from wilkpedia:


In 1967, Hathcock set the record for the 20th century's longest combat kill with a Browning M2 .50 BMG machine gun mounting a telescopic sight. The distance was 2,286 meters or 1.42 miles. Hathcock was one of several individuals to utilize the Browning M2 machine gun in the sniping role. This success led to the adoption of the .50 BMG cartridge as a viable anti-personnel and anti-equipment sniper round. Sniper rifles have been designed for this round.
The record stood until the 21st century, when in 2002 it was broken during Operation Anaconda in Afganistan by a Canadian three-man sniper team led by Master Corporal Graham Ragsdale from the Princess Patricia's Canadian Light Infantry (PPCLI). The record itself was set by Corporal Rob Furlong with a shot of 2,430 meters from a McMillan TAC-50 Long-Range Sniper Weapon on a Taliban fighter.