The Bulls were woeful from start to finish, with many of the 423 fans who made the journey leaving way before full time.
Chester - who are still unbeaten - went into the break 2-0 up. Akwasi Asante headed home in the 20th minute after Matty Hughes' effort was saved before Anthony Dudley fired home nine minutes later.
Things didn't get any better in the second half. Asante made it 3-0 in the 52nd minute and Danny Elliott headed home a fourth 12 minutes from time.
Hereford's consolation goal was from Jordan Cullinane-Liburd in stoppage time.
In truth, Hereford were lucky it was only four, with Chester having numerous opportunities to add to the scoreline.
We will post match reaction as soon as we get it, while a full report will go up in due course.