Mark Wright's side - re-instated in the competition after Bury had fielded an ineligible player in the last round - were far from overawed by opponents two divisions ahead of them, and actually had the better of the chances as they held on for a draw.
The visitors had sounded a warning with a 20-yard effort from Sylvain Legwinski, which had to be touched aside by keeper John Danby on six minutes, but from that moment on it was the Blues who enjoyed the better opportunities, although they had to withstand a late onslaught by Ipswich.
Chester had shown they were not going to roll over in a first half in which they had the lion's share of the play.
A swift attacking move by Chester on 15 minutes involved a neat one-two between Roberto Martinez and Gregg Blundell and ended with the ball in the back of the net, but the City striker had strayed marginally offside.
On 22 minutes Blundell wasted a gilt-edged chanced when an attempted pass, while he was in an offside position, deflected off Richard Naylor giving him a clear run on goal, only for his chip to beat the keeper but also the post.
Five minutes later it was Blundell in the clear again and his first-time shot was partially saved by keeper Shane Supple and the ball squirmed under his body and just inches past the upright.
Ipswich had their first decent chance on the half-hour mark when a swift counter-attack carved an opportunity for Matt Richards, only for Phil Bolland to produce an excellent block to deny him while Alan Lee pulled the rebound well wide.
On the stroke of half-time, Martinez cut in from the by-line and saw his effort from an acute angle saved by the keeper's legs.
Ipswich manager Jim Magilton had clearly given his side a rollicking at the interval and they showed more attacking intent in the first three minutes than they had in the whole of the first half.
Naylor was denied by a fine last-ditch interception by Ashley Westwood just as he looked set to put the ball in the net, and Lee saw his goalbound header pushed away with a full-length save by Danby.
Substitute Chris Casement was robbed of the ball in the right-back position on 58 minutes by Laurence Wilson, whose attempted chip didn't quite have enough height on it, allowing Supple to palm the ball away.
Jamie Hand rifled an effort just over the bar, and then hit a cross-shot which had the keeper back-pedalling to claim the ball on his goal-line. Blundell wasted another good chance with a wayward effort nine minutes from time.
But then Chester were on the back foot and, with six minutes remaining, Dan Harding cut through the Chester defence to set up Danny Haynes only for the substitute to hit his effort straight at Danby.
Striker Lee then struck the bar with a header with three minutes left, as Chester withstood the late pressure to earn a replay.