Putin -> Hamas -> Chechens

Putin is an old style Russian leader. He follows the principle "If everyone is against them, I should befriend them", hoping to gain favour and influence:

Until now, Russia has adhered to the quartet's common line, but Mr Putin's comments have sparked off speculation over whether Russia's policy towards the Israeli-Palestinian conflict has changed, the BBC's Steven Eke says.

With Hamas' electoral victory in January, Mr Putin may simply have perceived an opportunity to step in - and re-assert his country's influence - while others were considering how to respond, our correspondent says.

No matter that in the case of Hamas, even notorious Arab-lovers such as Spain and France are hesitant to start diplomatic ties right away.

No matter also that Hamas sees the Chechen insurrection as just another part of the global Jihad. Remember Beslan? All part of the same struggle against every infidel worldwide, as far as Hamas is concerned.
Ties between Hamas and the Chechen Jihadi's are well-documented:

According to the document, Hamas "is completely hostile to the Russian regime in that it identifies with the Chechen separatists, regarding them as part of the global jihad, and supports them in their terrorist activities."

The enemy of your enemy is not always your friend, Putin. In this case, the Enemy of your enemy is the Enemy of the whole world.