Although the Icelandic champions are making their debut in the competition, the second qualifying round tie is likely to be no laughing matter for the Scots as they attempt to make up for last season’s embarrassing performance.
Motherwell, Premier League rivals of Scottish champions Celtic, were among Stjarnan's victims as they progressed through three rounds of Europa League qualifiers before losing 9-0 on aggregate to Inter Milan last season.
Stjarnan won their first Icelandic league title in astonishing style in October, converting a stoppage-time penalty in their final game to beat FH 2-1 and finish one point ahead of their opponents.
The club once produced a bizarre goal celebration known as 'the fish' where the scorer would throw an imaginary fishing line and one of his team mates would pretend to be reeled in.
Although Stjarnan gained millions of YouTube hits for their antics, they have toned down the celebrations in the last two seasons.
Steaua Bucharest, the only other former winners in the draw for the first two qualifying rounds, face Slovak champions Trencin, with the first leg away.
Serbian champions Partizan Belgrade were paired with Georgia's Dila Gori and Bulgaria's Ludogorets Razgrad, who played in the group stage last season, play Moldova's Milsami Orhei.
The champions of 30 European countries enter the fray in the second qualifying round with the first legs on July 15/16 and the returns on July 21/22.
Last season Celtic, the 1967 European Cup winners, suffered the indignity of twice being knocked out of the competition.
They lost 6-1 on aggregate to Legia Warsaw in the third qualifying round but were reprieved after the Polish side fielded an ineligible player in the second leg.
After being reinstated, Celtic lost to Maribor in the playoff round.
(Writing by Brian Homewood, editing by Tony Jimenez)
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