The Iraq war was born in Grozny. Not the initial invasion where the US military dominated the battlespace, but the "insurgency" afterward.
Go forth and read this article: http://findarticles.com/p/articles/mi_m0IAV/is_2_91/ai_106792175/?tag=content;col1 and see that we didn't see the "writing on the wall" when it came to Iraq.
We really were the "arrogant Americans" in Iraq, at least at the policy level. The lessons of Chechnya are one to be studied at length by anyone who wants to be familiar with successful insurgent warfare tactics. Read this article written a scant 6 years after the first to compare/contrast: http://www.strategypage.com/htmw/htinf/20080731.aspx