Below is a particularly telling excerpt. Read the full document here, with thanks to John Derbyshire.
3. Any individual with another nationality (except for Israel) may obtain Iraqi nationality after a period of residency inside the borders of Iraq of not less than ten years for an Arab or twenty years for any other nationality, as long as he has good character and behavior, and has no criminal judgment against him from the Iraqi authorities during the time of his residency on the territory of the Iraqi republic.
4. An Iraqi may have more than one nationality as long as the nationality is not Israeli.