Republican Sen. Scott Brown and his Democratic challenger, Elizabeth WarrenElizabeth Ann WarrenOvernight Finance: Lawmakers grill Equifax chief over hack | Wells Fargo CEO defends bank's progress | Trump jokes Puerto Rico threw budget 'out of whack' | Mortgage tax fight tests industry clout Michelle Obama is exactly who the Democrats need to win big in 2020 Wells Fargo chief defends bank's progress in tense Senate hearing MORE, are running essentially even, according to a new poll from the Boston Globe.

Brown earned 39 percent support in the poll and Warren took 37 percent, a difference within the margin of error.

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Warren's campaign has been under siege for the controversy surrounding her claims of Native American heritage.

Earlier this week, Warren admitted she had told at least two former employers — Harvard University and the University of Pennsylvania — that she had Cherokee heritage, doing so after she'd already been hired. Warren has not substantiated that claim, aside from saying that her parents had repeatedly told her that her extended family tree included Native American blood.

Brown's campaign has been attacking Warren for not explaining the situation. 

"You know, you have to, especially in these type of things, when you’re checking a box and you’re getting benefits that are entitled to people who need them and who historically have been discriminated upon, and you have others relying on those representations, it is a problem," Brown said Thursday.

Seventy-two percent of those polled said the controversy would not affect their vote, while 23 percent said they would be less likely to vote for Warren because of it.

The Globe poll of 651 likely voters was taken between May 25 and May 31 and has a margin of error of plus or minus 3.8 percentage points.