Access to reconstruction contracts, access to Iraqi markets for their consumer goods, good PR and some gratitude from the Bush administration/US government, AND something that many people overlook: China has had problems in its western provinces with the various indigenous Islamic ethnic groups. Cooperation in Iraq helps China if turmoil in the Middle East is lessened, terrorist organizations are diminished so they can no longer pump arms and money into those provinces, and China is also probably entering into intelligence-sharing agreements with the US and others regarding terrorists.