The unofficial tally from the Donegal Electoral Area shows voting 54% Yes to 46% No.
This represents 44 boxes, or around one third of the Donegal South West constituency.
The areas returning a No vote were Donegal Town, Dunkineely, Frosses, Laghey and Ballintra.
Counting for the Glenties Electoral Area is now underway.
In one box on Arranmore Island, voting was 25 Yes, 25 No and one spoiled vote, according to unofficial tallies.
Overall, though, indications are that the vote on Arranmore was a Yes majority, 95 to 67.
DCC Cathoirleach Cllr John Campbell (Ind) and former Cllr John Boyle (FG) expressed “delight” at the early indications of a Yes majority.