Chester made the most of their FA Cup second chance, holding Coca-Cola Championship Ipswich to a goalless draw in a poor third-round tie at the Deva Stadium.
City were reinstated in the competition last month after their second-round opponents Bury fielded an ineligible player in their 3-1 replay win.
And the hosts could have booked an unlikely place in the fourth round had it not been for the heroics of Town goalkeeper Shane Supple, who made a number of crucial saves.
Chester manager Mark Wright included Ashley Westwood in his starting line-up after he shook off a hamstring complaint sustained during the 2-1 win over Notts County on New Year's Day, while Town made just one change - Supple taking over from Lewis Price in goal.
After a tepid opening City should have taken the lead in the 20th minute.
Gregg Blundell found himself one-on-one with Supple after a fortuitous ricochet off a Town defender fell into his path - but he could only drag his shot well wide.
Supple was again in the thick of the action moments later when he twice denied the hosts.
First he smothered another Blundell shot which squirmed under his body and out of play before holding a fierce Sean Hessey drive from the resultant corner.
Blundell then thought he had put his side in front when he poked the ball into the net but his effort was disallowed after he had strayed offside during the foray forward.
The visitors were again thankful to Supple on the stroke of half-time when he spread himself to make a wonderful save after influential City midfielder Roberto Martinez fired a low shot from inside the area.
Town manager Jim Magilton made one change at the break, replacing the ineffective Alex Bruce with Chris Casement .
His side began the second half with more urgency, with Lee stamping his quality on the contest with a couple of jinking runs.
But Town continued to undermine their hopes of finding a foothold in the game with some sloppy passing and poor individual errors.
Substitute Casement was almost left red-faced when he gifted the ball to Laurence Wilson - but his lobbed effort was turned away by Supple, who was forced to backtrack towards his own goal.
Magilton looked to stimulate his side into an attacking force in the 67th minute by replacing Billy Clarke and Matt Richards with Danny Haynes and Gavin Williams, who came on to score Town's winner against Birmingham on New Year's Day.
The game looked likely to meander towards a tame draw before Town embarked upon a late rally.
In the 83rd minute Dan Harding set up Haynes, who took his left-footed shot first time but his effort was too close to Danby - who gratefully held the shot to his chest.
And then moments later Town almost snatched a hardly-deserved winner when Lee saw a shot cannon off the crossbar.
Teams:
Chester Danby, Bolland, Artell, Westwood, Marples, Martinez,Hessey (Bennett 78), Hand, Wilson, Blundell, Walters.
Subs Not Used: Sandwith, Linwood, Rutherford, Holroyd.
Ipswich Supple, Bruce (Casement 46), De Vos, Naylor, Harding,Roberts, Legwinski, Garvan, Richards (Williams 68), Lee,Clarke (Haynes 68).
Subs Not Used: Price, Peters.
Booked: Clarke, Roberts.
Att: 4,330
Ref: J Moss (West Yorkshire).