Tennant hasn't yet entered the race, but speculation has swirled for months about whether she might run. Senate Majority Leader Harry Reid (D-Nev.) said this month that he believes Democrats will be "very competitive in" West Virginia, and that "we have a candidate there who should be announcing shortly."
In the poll, Capito gets 45 percent support to Tennant's 40 percent support. Fifteen percent remain undecided.
Democrats and Republicans alike have criticized the poll's methodology, charging that the sample size — 400 people — was too small, and that the results may not be accurate because respondents weren't screened for whether they're likely to vote, or spread evenly across the state.
They also charge that the sample size may overall have a higher level of education and higher income level than the state in actuality.
The survey was conducted among 400 West Virginia adults from Aug. 15-22, and has a 4.9 percentage point margin of error.
Poll: W.Va. secretary of state would make Senate race competitive
The West Virginia Poll, conducted by the nonpartisan R.L. Repass and Partners for the Charleston Daily Mail, gives Rep. Shelley Moore Capito (R) — the leading Republican in the race — a five-percentage-point lead over Tennant.