Remain and Leave are both on 41%, with 18% don't know or won't vote, according to the latest YouGov survey for ITV Wales and Cardiff University.
YouGov polls on the issue since 2013 have shown very close results.
Professor Roger Scully said the race was tight as many Labour and Plaid Cymru voters did not agree with the pro-EU views of their party leaders.
An in-out referendum on the UK's relationship with the 28-member bloc will be held on 23 June.
"With little more than two weeks to go, this new poll suggests that things could not be closer in Wales," said Mr Scully, of the university's Wales Governance Centre.
"Despite the vast majority of the political establishment in Wales supporting a Remain vote, it is now looking very possible that Leave could carry the day here, with many Labour and Plaid Cymru supporters apparently intending to defy the leaders of their parties and vote for Leave."
The survey was carried out from 30 May to 2 June and included a representative sample of 1,017 Welsh adults.
Laura Ann Jones of Vote Leave Cymru said: "This poll suggests that the campaigns are now neck and neck, with voters increasingly rejecting the negativity of 'Project Fear' and embracing a positive future for Wales and the UK outside of the EU."
A Wales Stronger In Europe spokesperson said:  "This poll just confirms what we've always known - that the referendum is close, and every vote will count.
"With so many people still undecided, we will continue making the case for a Wales that is stronger, safer and better off in Europe."
The two sides of the debate over the UK's future in the EU are "dead level" in Wales, a political expert has said.