Iraqi President Jalal Talabani was one of the first to cast a ballot. He told Radio Free Iraq the referendum is a milestone in Iraq's transition to democracy.
"Today is a feast, the constitution feast," he said. "I remember when in my youth we would rise early in the morning to wear new clothes in celebration of the feast. God willing, today's feast will be a beginning to build Iraq on democratic foundations as an independent, federal and prosperous country. God willing, the constitution will serve as a factor for unifying all Iraqis, for strengthening national unity and bolstering Iraq's stability."
Security is tight for today's vote. Tens of thousands of Iraqi police and soldiers are protecting 6,000 polling stations, with U.S. and other foreign troops ready to help out if needed.
International borders were sealed earlier this week, and shops and businesses have been closed since 13 October.
There has been some violence -- three Iraqi soldiers were killed by a bomb north of Baghdad and clashes were reported in the western city of Al-Ramadi.
But overall security appears to be holding, and reports suggest there's been a steady stream of voters. "We come to cast our votes on the constitution," said one voter in Baghdad. "This is a great day for the stability of our country and it will be an unforgettable day."
The last time Iraqis voted in a referendum was three years ago, under Saddam Hussein's rule. The regime said 100 percent voted to renew Saddam Hussein's leadership for another seven years.
This time the outcome is a lot less certain.
Kurds and Shi'a mostly support the charter, but many Sunnis oppose it. They fear federal provisions could lead to the break-up of Iraq and deprive Sunnis of a share in the country's oil wealth.
However, last week one Sunni Arab party decided to back the draft, after Shi'ite and Kurdish leaders agreed to consider amendments next year. That may be enough to split the Sunni vote -- and that would mean a "no" vote is less likely.
Talabani said the constitution best serves most of Iraq's people. "I think this constitution represents most of the Iraqi people's aspirations," he said. "I would not claim that the constitution is perfect but it is the best that could be drafted at this stage. It is one of the best constitutions in the Middle east."
A simple majority needs to vote "yes" for the draft constitution to be approved. If two-thirds vote "no" in any three of Iraq's 18 provinces, it will be rejected.
Approval would clear the way for Iraq to hold its first national elections for a full, four-year government in December.
Failure would mean that the election in December would elect only an interim assembly, charged with drafting a new constitution from scratch.
(Radio Free Iraq/ news agencies)For RFE/RL's full coverage of Iraq's constitutional referendum, see "Iraq Votes 2005"