Aside from a few outliers, the poll, conducted by Rasmussen Reports, is the latest to show the former governors and Virginia political heavyweights in a virtual dead heat as they compete for the seat of retiring Sen. Jim Webb, a Democrat.
Four percent of respondents preferred another candidate in the race, and 5 percent were undecided.
The survey of 500 likely voters was conducted April 23, and the margin of error is 4.5 percentage points.
Mr. Kaine is running unopposed for the Democratic nomination, while Mr. Allen faces a primary challenge from tea party activist Jamie Radtke, Chesapeake Bishop E.W. Jackson, and Delegate Robert G. Marshall, Prince William Republican.
The Republican Party of Virginia hosts the first of three GOP primary debates Saturday at 3 p.m. at the Sheraton Roanoke Hotel and Conference Center in Roanoke. All four Republican candidates will participate.
The party announced Tuesday that Jay Warren of WSLS-TV will moderate the 60-minute debate. The panelists will be Dave Suetterlein, Roanoke County Republican Committee chairman; Miki Miller, president of the Virginia Federation of Republican Women; and Michael Cogar, chairman of the College Republican Federation of Virginia.
Each participant will get the opportunity to make two-minute opening and closing statements. They will get 90 seconds to respond to each question, and all candidates will answer the same questions.
The first and last question will be asked by the moderator, and all other questions will be asked by the panelists.