Nine players were shown yellow cards as nerves seemed to get the better of both teams. Goalscoring opportunities were few and far between as both defences remained comfortably in control.
Chester did manage to get the ball into the Swansea net, but David Flitcroft's effort was ruled out for offside. Ten minutes from the end Andy Milner squandered the home side's best chance of a goal when he failed to connect as he tried to convert Flitcroft's cross.
Swansea's best effort came as early as the fourth minute, when Jonathan Coates had a weak shot easily saved by the Chester goalkeeper, Ronnie Sinclair.
The Chester manager, Kevin Ratcliffe, still has high hopes of reaching Wembley. "We're confident of winning because we can always score away from home," he said.
However, on this evidence Jan Molby's side look the better bet for the final as they prepare for Wednesday's second leg at the Vetch Field.
Chester City: Sinclair; Davidson, Jenkins, Reid, Woods, Alsford, Flitcroft, Priest, McDonald, Milner, Aiston. Substitutes not used: Fisher, Brown, Rimmer.
Swansea City: Freestone, Thomas (Heggs, 55), Moreira, Walker, Edwards, Jones, Appleby, Penney, Torpey, Ampadu, Coates. Substitutes not used: Chapple, Jenkins.
Referee: C R Wilkes (Gloucester).
Bookings: Chester: Reid, Woods, McDonald, Flitcroft. Swansea: Jones, Edwards, Penney, Ampadu, Torpey.
Attendance: 5,104.Reuse content