A new opinion poll for Survation has found a 50/50 split between support for remaining or leaving the UK.
When undecided respondents are included, there is a 45/45 split, with one-in-ten voters unsure how they would vote in a divisive second independence referendum.
The new figures come despite a relentless campaign from the SNP in recent weeks.
Pamela Nash, chief executive of Scotland in Union, said:
“With one-in-ten Scots undecided, this poll is a reminder to those of us who believe in solidarity and oppose division that we must continue to make the positive case for remaining in the UK every day.
“We know the overwhelming majority of people in Scotland don’t want a divisive second independence referendum this year, but Nicola Sturgeon is ramping up her campaign in a desperate bid to deflect from the SNP’s failings in office.
“She should stop trying to divide Scotland and focus on fixing the public services her government has run into the ground. Scotland deserves better.”