Well, the main points have already been addressed, but I’d like to add that there is some question (actually, a big question) whether Chechnya would be a halfway viable independent state. Even before the past 10 years worth of conflicts and mass refugee movements, there were only a million-ish inhabitants of Chechnya, not all of whom were Chechen. Some further sources:
Allen, W.E.D., and Muratoff, Paul. Caucasian Battlefields: A History of the Wars on the Turco-Caucasian Border, 1828-1921. Cambridge University Press: Cambridge, England, 1953.
Bennigsen, Alexandre, and Wimbush, S. Enders. Muslim National Communism in the Soviet Union: A Revolutionary Strategy for the Colonial World. University of Chicago Press: Chicago and London, 1979.
Broxup, Marie Bennigsen (ed.) The North Caucasus Barrier: The Russian Advance towards the Muslim World. Hurst & Company: London, 1992.
Gammer, Moshe. Muslim Resistance to the Tsar: Shamil and the Conquest of Chechnia and Dagestan. Frank Cass c/o International Specialized Book Services, Inc.: Portland, Oregon, 1994.
Geiger, Bernhard; Halasi-Kun, Tibor; Kuipers, Aert N.; Menges, Karl H. Peoples and Languages of the Caucasus. Mouton & Co.: Gravenhage, 1959.
Karklins, Rasma. Ethnic Relations in the USSR: The Perspective from Below. Boston: Allen & Unwin, 1986.
Kirkwood, Michael. “Glasnost’, `The National Question,’ and Soviet Language Policy.” Soviet Studies, vol. 43, no. 1, 1991, pp. 61-81.
“Russian Federation: Ethnic Discrimination in Southern Russia,” Human Rights Watch, August 1998. Retrieved from http://www.hrw.org/reports98/russia/ on 11/2/99.
Simon, Gerhard. Nationalism and Policy Toward the Nationalities in the Soviet Union: From Totalitarian Dictatorship to Post-Stalinist Society. Westview Press: Boulder, San Francisco, and Oxford, 1991.
Weinreich, Uriel. “The Russification of Soviet Minority Languages.” Problems of Communism vol. 2, no. 6, 1953, pp. 46-57.
Wixman, Ronald. Language Aspects of Ethnic Patterns and Processes in the North Caucasus. University of Chicago Press: Chicago, 1980.
-----. The Peoples of the USSR: An Ethnographic Handbook. M.E. Sharpe: Armonk, NY, 1984.
And some links:
Ethnolinguistic map of the North Caucasus (somewhat outdated now, but still cool):
Chechnya maps:
http://www.lib.utexas.edu/maps/chechen.html
Lots more maps at UT/Austin:
http://www.lib.utexas.edu/maps/commonwealth.html
Russian Federation population statistics:
http://polyglot.lss.wisc.edu/creeca/kaiser/popul.html
The Red Book of the Peoples of the Russian Empire (sort of the endangered species list of ethnicities):
http://www.eki.ee/books/redbook/
The Russian Constitution (in English - check out Chapter 3, whch explains the administrative structure a bit):
http://www.constitution.ru/en/10003000-01.htm
What specifically are you interested in?