The latest Steadman poll gave Odinga 43.6 percent to Kibaki's 43.3 percent. Its last poll two weeks ago showed Odinga with 45 percent and Kibaki with 41 percent.
Since then, the 76-year-old incumbent has stepped up his appearances in towns and villages across east Africa's biggest economy. He has even curtailed an official visit to Uganda for a Commonwealth meeting to return to the campaign trail.
"There is what we can call a hairline difference between the two top contenders," George Waititu, Steadman managing director, told reporters.
"Voter turnout will still be the biggest determinant in terms of who wins," he added.
Kenya's parliamentary and presidential polls take place on Dec 27.
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