With seven birdies in the first 10 holes, Jeev had a chance to bring home a career-best round and even entertain thoughts of the magic number of 59, but in the end he settled for a 65 here.
Jeev, who is winless since 2008, was one shot ahead of Mark Foster, Andrew Marshall and Matthew Zions, all of whom shot 66 each in the opening round.
Out on the world famous links, Jeev went to the turn in a six-under 30 and with another birdie at the long tenth led the tournament by one.
But he dropped a shot on the par-3 14th but picked a birdie on the 18th to finish at 65 and as the leader.
On the front nine, Jeev birdied three in a row from second to fourth and then added a fourth on the sixth hole. He then followed it up with birdies on eighth, ninth and tenth holes to go to seven-under.
England's Mark Foster was the early clubhouse leader as the Irish Open returned to Northern Ireland after a gap of 59 years.
Padraig Harrington shot a 67 as did defending champion Simon Dyson. Scot Paul Lawrie, third in The Ryder Cup points table, and European Captain Jos
