There probably are, but I can't find any information on them. I asked my Russian friends and they said they also have no idea about Chechens. I guess, got to find a Chechen friend then.

You see, there in Moscow now are a lot of also other souther national criminal groups, like Georgian, Uzbek and others.

Anyway, about Chechens in Moscow. I found two articles in Russian on kompromat.

In the 90's there were 3 groups that were operating in Moscow:
Tsentralniy OPG - leader Lecha Islamov, controls around 300 businesses, men and women prostitution in central hotels and markets.
Ostankinskiy OPG - leader Mahmud "Bolshoi", controls furniture sales, as well other products, computers, their delivery to Grozny
Yuzhnoportoviy OPG - leader Nikolay "Hoza" Suleimanov, controls vehicle business in the city.