From Strobe Talbott's "Russia Hand", it's clear that the official U.S. supported Russia's Government during the First Chechen war, fought in 1994-1996:
"What little we did know about Chechnya and Dudayev inclined us to accept Moscow's version that it was dealing with an ugly mixture of secessionism and criminality. Besides, the independence that the Chechens were fighting for was against American policy. As a global principle, we were for federalist solutions that preserved existing international boundaries and against the fractionation of large, heterogeneous countries into ethnically based microstates. Hence Gore's terse public comment in Moscow: 'We are following [the situation] closely. We hope very much it can be solved by negotiations. We believe it is an internal matter.' "
They even went that far as to compare the First Chechen War to the American Civil War, when explaining the situation to the press.