Chester have missed some glorious opportunities but it remains goalless at Edgar Street.
In the fifth minute, Dino Visser saved from Charlie Caton before Kurt Willoughby somehow put the rebound wide. Willoughby had another chance in the 21st minute but he blazed his effort high and wide before Visser saved from Rhys Hughes.
Hereford had their best opportunities on the stroke of half time. Thierry Latty-Fairweather shot just wide before Levi Andoh fired over.