Neil Lennon's side endured a frustrating night at Parkhead as they were held goalless by a stuffy visiting side.
Much of the talk before the game concerned the visitors' starting line-up which contained two players who had been deemed ineligible by FIFA after the club broke a signing embargo.
But the Swiss Cup winners produced a battling performance on the pitch as the Hoops struggled to break down their packed defence.
Celtic found Sion goalkeeper Andris Vanins just too formidable a barrier to pass.
The slick-passing visitors proved more than a match for the host although Celtic had their chances.
However, in a frustrating night in the east end of Glasgow, Sion's inspired number one had good saves from Charlie Mulgrew, Kris Commons and substitute Shaun Maloney to keep the tie in the balance ahead of the second leg next week in Switzerland next week.
Commons had a close-range header saved by the Sion goalkeeper after climbing high at the back post to reach a Cha Du-Ri cross.
Maloney was brought down 25 yards from goal by Jose Adailton and his free-kick had Vanins diving down to his right-hand post to keep the ball out and Georgios Samaras' attempt from the rebound.
The Hoops players trooped off to the sound of boos from their own supporters, who will view next week's return match in Switzerland with some trepidation.