Greek polling stations will remain open until 7pm local time for the first referendum there in 4 decades.
The people are being asked if they support or reject the terms of a bailout loan which has since expired.
Up until recently, polls showed greater support for the government's position in rejecting the deal, but in recent days the Yes side appear to have the upper hand by a very small margin.
Irish politicians Paul Murphy and Pearse Doherty, have traveled to Greece for today's vote.
The Socialist and Sinn Féin TDs, are both hopeful that Greece will reject the terms of the bailout deal with the Troika.
Speaking from Athens, Paul Murphy says the outcome is likely to be a close one:
