Name: Sinopec (China Petroleum & Chemical Corporation)
Based in: China
According to Wikipedia, Sinopec is listed in Hong Kong and also trades in Shanghai and New York; Sinopec Limited's parent, Sinopec Group, is the world's largest oil refining, gas and petrochemical conglomerate.
Fields in Iraq: Mansuriyah, Sumer
From the company's website:
"China Petroleum & Chemical Corporation is a vertically integrated energy & chemical company that is engaged in oil & gas exploration and production."
For latest news on this company's activities in Iraq please click here.
A full list of International Oil Companies (IOCs) operating in Iraq under licences granted by the Ministry of Oil in Baghdad can be found here.