The Glasgow man picked up birdies at the first, second and fourth holes during a solid round of 69 which contained just one bogey. That glitch came at the 15th but Jamieson recovered quickly to pick up another birdie at the 16th.
His three-under par total leaves him in a tie for ninth place, two shots behind leader Ryan Fox of New Zealand.
Fellow Scots Marc Warren and Richie Ramsay also enjoyed a good day in Donegal. The pair are a stroke further back after both returned scores of two-under par 70.
Aberdonian Ramsay had birdies on four, 15 and 16 but was left to rue a dropped shot on the penultimate hole. Warren, meanwhile, had a round of two halves, picking up four birdies on his front nine but bogeying two on the inward half.
Russell Knox, runner-up at the Open de France last week, is one under after a round of 71. Connor Syme is a shot further back after a 72.
David Drysdale is four over after a 76; Stephen Gallacher shot 78 and Bradley Neil 79.
l Adri Arnaus was the star of the show on a lightning-affected opening day of the Prague Golf Challenge at Prague City Golf, carding a nine under par 63 to hold a two-shot lead.
Scots David Law, Ewen Ferguson and Ross Kellett are six shots off the lead after all three had opening rounds of 69. Compatriots Robert Macintyre and Liam Johnston are one further back after 70s.