That's ridiculous. Exxon and Chevron are in Iraq. Didn't you see the list that Pandavoine posted yesterday? Well here it is again just in case you didn't read it.
From Pandavoine:
The following is a list of International Oil Companies (IOCs) operating in Iraq under licences granted by the Ministry of Oil in Baghdad:
BP Chevron Corporation China National Offshore Oil Corporation (CNOOC) China National Petroleum Corporation (CNPC) DNO International Dragon Oil Eni ExxonMobil Gazprom Genel Energy Heritage Oil Hunt Oil Inpex Japan Petroleum Exploration Company (Japex) KazMunaiGas (KMG) Kogas (Korea Gas Corporation) Kuwait Energy Company Lukoil Marathon Oil Corporation Occidental Petroleum Pakistan Petroleum Petronas Shell Sonangol Statoil Talisman Energy Total Türkiye Petrolleri Anonim Ortakligi (TPAO)