Promotion-chasing Bradford dominated play especially after the break but they could find no way past Danby, who blocked Graeme Lee's far post shot deep in injury time.
The Bantams had hoped to kick-start their Christmas schedule with a home win, but they failed to sparkle in the opening period despite a couple of teasing crosses from on-loan winger Steve Jones.
Bradford defender Matt Clarke made a crucial tackle on Chester striker Kevin Ellison as he charged down on Rhys Evans' goal, but it was 45 minutes before Danby was tested by a Bantams' attack.
After some neat approach play by the home side, Jones, who is yet to score for his new club, let fly from the angle of the box but Danby had his shot well covered.
Soon after the interval, Danby produced a super save to keep out Jones' low drive and his agility was almost rewarded when team-mate Mark Hughes saw an overhead kick drift just over the Bradford bar.
Bradford, who could have jumped into second spot with a victory, pressed forward late in a bid to break the deadlock but Chester refused to buckle.
The visitors survived a few late scares and Danby was grateful to see Omar Daley's snapshot hit his legs after a scramble in the box with only three minutes left of normal time.
In a frantic period of injury time, the Chester keeper capped his fine display by getting himself in the perfect position to deny Bradford skipper Lee as he looked to force the ball home from six yards out.