In a game of very few chances, Steed Malbranque and Gael Danic came closest to opening the scoring.
Chornomorets were impressive, however, and could even have snatched a precious win when Kirill Kovalchuk narrowly missed the target from 20 yards.
Remi Garde's Lyon team went into the game with eight wins from their last 10 matches and will be frustrated not to have scored against a side who have not played in the Ukrainian league since the beginning of December.
Lyon's starting line-up had only managed 65 starts in the French league between them so far this season, with their Serbian captain, Milan Bisevac, the only first-team regular.
A crowd of 26,250 were at the Chernomorets Stadium and they witnessed a quiet first-half.
Chornomorets enjoyed a lot of possession in the opposing half but they were unable to test Lyon goalkeeper Remy Vercoutre.
It was Lyon who had the best chance in the opening half, though, when in the 28th minute Malbranque forced Yevhen Past in the Chornomorets goal into a splendid save with a powerful shot from 12 yards.
The French side started the second-half brightly and Malbranque tried to curl a chance in from the edge of the area, only for Past to calmly collect the ball.
Roman Grygorchuk's side responded quickly, with Kovalchuk and Anderson Mineiro both going close.
Lyon's Danic was the best player on the pitch but, despite having three good chances, he was unable to break the deadlock.