Commissioned by tycoon Sir Tom Hunter for the launch of a project giving voters impartial information about their options, the survey suggests a five-point swing toward independence among decided voters since the autumn.
The TNS poll put support for independence at 29%, with support for the Union at 42%, and 29% of voters saying they were undecided. However, leaving aside the "don't knows", support for Yes among decided voters was 41% - up from the 36% recorded by TNS in October.
The poll also found 69% of voters believed David Cameron should debate the key issues with First Minister Alex Salmond, something the Prime Minister steadfastly refuses to do.
Although support for a debate was highest among SNP supporters - who hope Cameron's appearance would backfire and boost the Yes vote - 60% of those voting No also wanted to see a debate, including a majority of Tory voters. Only 17% of those polled were against a debate.
TNS found 56% felt they lacked the information to make up their mind, and that only one in seven had read any of the White Paper on independence: half of those aged 16 to 24 had never even heard of the White Paper, published in November.