The visitors had much the better of the game but the football failed to match the perfect weather.
The closest either team came to breaking the deadlock was three minutes from the end when Shrewsbury substitute Andy Cooke volleyed against the bar.
Shrewsbury started well with Michael Jones' free-kick going narrowly wide and Dave Edwards forcing a good save from Chester keeper John Danby.
Nine minutes before the break confusion in the Chester defence let in Derek Asamoah, who shot goalwards but skipper Dave Artell cleared at full stretch with Danby nowhere.
Perhaps the most potent statistic from a very scrappy first half was the fact that seven balls were kicked out of the ground.
The Shrewsbury supporters turned out in great numbers, bringing nearly 1,800 fans out of a total attendance of just 3,266.
Chester's young striker Chris Holroyd should have done better when put clean through shortly after half-time but he could only shoot tamely at keeper Scott Shearer.
At the other end, Danby was called into action to keep out Asamoah's sweetly struck free-kick and then picked himself up to block Cooke's close-range rebound.
Shrewsbury had the ball in the net after 70 minutes when Danby failed to clear under his own crossbar, but referee Paul Taylor ruled it out for a push on the keeper by Kelvin Langmead.
Deep into the six minutes of injury-time, Chester nearly won it when Alex Meechan's cross was kept out by the legs of Shearer who knew little about it.
Shrewsbury dominated possession as the game wore on, but in truth neither team deserved the points.