Rather than Chechnya, the game largely takes place in Urzikstan which is also located in the Caucasus, was invaded by Russia in the 90s and features clashing between secular nationalists and Islamists. Furthermore, Urzikstan's flag closely resembles the Republic of Ichkeria's.
Urzikstan (Arabic: #H12JC3*'F) is a fictional country featured in Call of Duty: Modern Warfare, Call of Duty: Modern Warfare II, and Call of Duty: Modern Warfare III.