It's complicated, Katie. In short Chechnya is predominately Muslim and had been under Soviet (read godless here) rule for decades. When glasnost hit Russia and their control over the other countries and territories slackened, the Islamic separatists in Chechnya saw this as their time to agitate for an independent Islamic state.
Couple this with an American effort to foment trouble in the Soviet Union's backyard by providing varying amounts of assistence to this rebels prior to and after the destruction of the Wall and it starts getting complicated. Now that we are in a full blown war with terrorism which largely equates to squashing Muslim extremism, it becomes our problem as well since we want Russia's help in fighting this problem.
Finally, to further muddy the waters, Russia did not join with us against Iraq (for completely different reasons than what was happening in Chechnya, namely money interests) and Afganistan (because of their previous involvement there) which emboldened the rebels and caused a greater rift between our two countries on the whole war on terrorism thing.
Like I said, it's complicated.
Totem