The Russian Defence Ministry said the Mi-24 combat helicopter was downed near the south-eastern village of Meskety.
It is not immediately clear what brought the aircraft down, although Russian military sources said it appeared that either a missile fired from a shoulder-held grenade launcher or a rocket fired from a launcher was used, the official Russian news agency Tass reported.
The helicopter was one of a pair escorting a Mi8 transport helicopter on a mission to deliver food to military units in mountainous areas when it dropped out of sight, a defence ministry spokesman told Reuters news agency.
The remaining aircraft returned to circle the area and saw the debris of the downed aircraft.
Second disaster
Chechen rebels are reported to have claimed responsibility on their website, and also said their fighters had visited the crash site and stolen weapons.
Russian authorities said troops were combing the area searching for possible suspects.
The incident comes less than two weeks after a large military transport helicopter was shot down by a missile in Chechnya, with the loss of 118 lives - Russia's worst military aviation disaster.
President Vladimir Putin accused the Russian military following the disaster of not following correct procedures and has vowed to carry out military reforms.
Defence Minister Sergei Ivanov has said members of the Russian military found responsible for the incident because of breaches of discipline or "sloppy" behaviour would be severely punished.