After equalising, they threatened to snatch victory from a match which could so easily have been beyond their reach at half-time.
After a couple of early scares, Chorley dominated the first hour, the first half in particular, and on another day could have gone to the break with the points in the bag.
That they did not do so was down to superb goalkeeping by Avenue’s Jonny Saltmer and some brave last-ditch defending by the visitors in front of goal.
Bradford were quick on the break from the start and Nicky Clee forced Matt Urwin to tip over a fierce drive before the visitors should have gone ahead on 13 minutes.
Jon Ustabasi carelessly tripped Clee just inside the box but Oli Johnson wasted the spot-kick, firing high over the bar with a replica of a recent Bruno Fernandes penalty for Manchester United.
Chorley took heart from the miss and Ustabasi quickly made up for his misjudgement with a brilliant solo goal on 21 minutes. He embarked on a twist-and-turn run past two defenders before whipping a superb shot into the corner of the net.
Only a terrific save by Saltmer from a close-range Mike Calveley header and two desperate blocks in the jaws of goal from successive shots, followed by another reflex save from a rising Billy Whitehouse drive kept Bradford in the game at the break.
To their credit, hard-working Bradford restricted the Magpies’ shooting chances in the second half, though they were relieved to see a smart angled header from Connor Hall pass just beyond the post with Saltmer beaten.
The visitors continued to probe in breakaways and in the last fifteen minutes forced a series of corners from one of which in the 79th minute substitute Luke Rawson nipped in to plant a header just inside the near post.
This equaliser gave Avenue real hope that they could go on to win and the Magpies were indebted to Urwin for a double save in the closing minutes which at least preserved a point from a game which overall ought to have brought Chorley three.
CHORLEY : Urwin, Henley, Smith, baines, Blakeman, Tomlinson, Calveley, Whitehouse, Ustabasi (Shenton 51), Hall, Blyth (Alli 81).
Unused subs. Okome, Leather, Scarborough.
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