There is information that says that the Chechen rebels are funded by the FSB and SVR. It is sketchy, but could hold true.
Look here:
here is some info for you
Bin Laden aide had KGB link
http://209.157.64.200/focus/f-news/1461070/posts
To The Qaeda:Ex Russian Agent, Vice Bin Laden Trained From Kgb
http://www.freerepublic.com/focus/f-news/1461064/posts
http://news.webindia123.com/news/showdetails.asp?id=98038&cat=World
Russian secret agency FSB trained Al Qaeda's al-Zawahiri: Report:-
http://www.mosnews.com/news/2005/07/18/fsbalqaeda.shtml
Al Qaedas Al-Zawahiri Received Terrorist Training in Russia Newspaper
KGB trained Zawahiri, says former agent
http://www.dawn.com/2005/07/17/int14.htm
I am not sure they do it directly, but what is certain is that the army generals deal big time in arms and ammunition with the Chechens.
The whole war is a big business: you bomb a city into rubble, then the central government says "Chechnya is part of Russia, we must reconstruct the place for the population's sake" and signs huge funds for the purpose.
These funds are stolen by the officials (and lion's share of them finds its way to the Swiss accounts of the main actors), then the "rebels" duly perform another terrorist act which is replied to by another bombing... so all the traces of the theft are well covered by the rubble.
Isn't it a nice, flawless scheme?