The dark horse in a blue suit

It's 9 p.m. in an industrial compound in Baghdad's once-mean but still volatile Daura neighborhood. Dathar al-Kashab, dressed in his trademark blue coveralls, orders his staff with the precision needed to oversee the expansion of the country's second largest refinery.

On this night, however, his staff are the family and friends that makeup an outsider's campaign for a seat in Parliament, one week from pivotal national elections March 7.

Kashab, the director general of Iraq's Midland Refine...