I think it is pretty much common knowledge in Russia that the Chechen terrorists are financed from Saudi Arabia and Qatar (the same sources which finance the rebellion in Syria).
Several notable terrorists killed in Chechen Republic came from Saudi Arabia, such as Ibn al-Khattab.
In this video, popular Russian observer and blogger aka "El-Murid" explains his point of view that the Second Chechen war was won by Russia only after they killed the key Arab figures such as the mentioned Khattab, through whom the money were distributed.
Once they were killed, the warlords sent their own emissaries to Saudi Arabia and Qatar, but their unity was lost because there was no longer single money distribution center.
Note, it is another well known fact that rebel leader Yandarbiyev was killed by Russian secret services in Qatar.
According some rumors (El Murid also says this), Qatar currently stopped financing terrorists due to dynastic succession, and as such, Saudi Arabia remains the main source.