The latest opinion poll for The Sunday Times has yes at 51% with 49% voting no.
It's the only poll with a lead for the Yes campaign, but many others have shown a narrowing of the gap between the two sides.
Scots will be asked the yes/no question 'should Scotland be and independent country?' on September 18th.
Issues such as nuclear weapons and the high number of food banks in Scotland are the main concerns for Christians in the group.
But, despite the polls showing a yes lead, Christians for Independence has urged campaigners to continue working until referendum day.
The group's tweeted: "As Casey Kasem would always say: "Keep your feet on the ground and keep reaching for the stars." Long way to go #sundaytimespoll #indyref"
The narrowing of the polls follows a number of blunders by the No campaign including a claim in a leaflet that the cost of shopping would increase following independence.
Supermarket chain Tesco said this was not true.
But the No campaign is stepping up its push for votes.
It's reported the Conservative and Liberal Democrat parties will step back and let Labour lead the campaign.
It's thought Chancellor George Osborne will also offer a timetable for new powers following a no vote.
Tory London mayor Boris Johnson told The Daily Telegraph Scotland going independent would be "an utter catastrophe".
He said: "We are on the verge of trashing our global name and brand in an act of self-mutilation that will leave our international rivals stunned, gleeful and discreetly scornful".
The Better Together campaign says only the union can bring success to Scotland but the Yes campaign says only the powers of independence can improve the country.
Premier will be broadcasting live from Scotland over the referendum.