Kenyan Prime Minister Raila Odinga has predicted a landslide victory for the proposed constitution in a national referendum.
Mr. Odinga cast his vote early Wednesday at a school in Kibera, Africa's largest slum and home to more than one million residents in western Nairobi.
Kibera residents, part of Mr. Odinga's constituency as a member of parliament, turned up in large numbers to greet the popular leader as he entered the polling station.
The prime minister has been one of the leading figures of the "Yes" campaign, urging Kenyans to approve the proposed constitution in the nationwide referendum.
After voting, the prime minister told reporters the vote was an historic moment for Kenya.
"From the reports I have received, it is peaceful all over the country," he said. "And I want it to remain that way so that Kenyans can peacefully decide their future. I have no doubt in my mind that the 'Yes' is going to win resoundingly. I want to predict over 70 percent victory."
Recent polling figures appear to support the prime minister's forecast. More than 60 percent of Kenyans say they support the new constitution.
But a spokesperson for the 'No' campaign, Chris Foot, says the vote will be much closer than expected.
"I think it is going to come down to the wire," said Foot. "I think the polls which have been out over the last few weeks, I do not think they have been entirely accurate. So I think that people will be surprised. But in the final analysis, with the amount of money the government has spent, it would be very unlikely that the 'Yes' do not win."
The referendum is a critical part of an agreement that ended violence after Kenya's presidential election in December of 2007. The agreement produced a Government of National Unity and set in motion the process of constitutional reform.
Many in the country hope to complete that process when the Interim Independent Electoral Commission announces the results of the vote Thursday.