The Mi-8 helicopter hit the power line while conducting a routine low altitude flight in the suburbs of Grozny, said Chechen Deputy Interior Minister Sultan Satuyev.
There were no reasons to suspect that the helicopter came under hostile fire from the ground, he added.
The weather was good at the time of the crash and he attributed the incident to either technical problems or pilot error.
Preliminary reports suggest the helicopter -- with 12 passengers and three crewmembers -- belonged to the border guard forces that operate under the authority of the Russian Federal Security Service.