The quest to reach the semi-finals of the Scottish League Cup still hangs in the balance as Hearts and Celtic are playing out a goalless draw at Tynecastle at the break.
Robbie Neilson's men had the first opening of the match when Juanma nodded the ball into the path of Osman Sow, but his low strike proved to be tame and straight at Craig Gordon.
The Bhoys pressed back at the home side and Stuart Armstrong found an opening for a drive at goal, which was deflected inches past the post.
Armstrong turned provider minutes later when he raided down the right and sent a cross into the box for the run of Leigh Griffiths, but the forward sent his effort off target.
Sow could have put the home side ahead when he latched on to a through-ball behind the Celtic defence, but with only Gordon to beat he sent his effort trickling past the post.
Jordan McGhee threatened before the break as he collected the ball down the left and fired a low effort towards the bottom corner which drifted just wide.