Hereford were frustrated by high-flying Chorley, who scored an early goal and then shut down the Bulls.
It was a typical away performance from the side in third place. Jack Hazlehurst scored the opener, finding space in the box to convert a long throw.
Hereford had chances, with a Yusifu Ceesay free-kick pushed around the post. But ultimately, they struggled to land a blow to get themselves back on level terms.