REUTERS/Marcos Brindicci
The ORB poll for the Telegraph found that 51% of voters now support the Remain campaign, while just 44% of voters support Leave.
However, ORB also asked the people they polled how likely they were to actually turn out and vote.
ORB used this information to recalculate their figures and found that support for Remain in 49% and Leave 48%.
The key reason that the Leave campaign is still so close to Remain is that its supports are much more likely to say that they will definitely vote. 70% of Leave voters say they will go to the polling booth, while just 61% of Remain supporters say they will turn out to vote.
Both campaigns will be worried that when ORB carried out the same poll last month, more of their supporters said they would definitely vote. The proportion of Remain backers saying that they are certain to vote has fallen 11%, while the proportion of Leave voters saying they are certain to vote has drop by 9% .
When you combine the falling voting intention with another factor - that 87% of people say that if they do turn out to vote, they have already made up their mind, the challenge for both campaigns becomes clear.
The side who will win the EU referendum will be the one that convinces their supporters to actually turn up to vote on June 23.