Simon Yeo had skied his penalty effort over the bar and Kevin Roberts had seen his effort saved by keeper Paul Smith after the hard-fought game had finished goalless.
Despite the lack of goals during the game, both sides had looked to play entertaining passing football and several chances went begging at each end, including a Grant Holt penalty miss five minutes from the end of normal time.
In the sixth minute Chester keeper John Danby had been called into action to produce a fine save to deny Holt.
For Chester, Jamie Hand struck a free-kick which took a deflection and was well saved by Smith.
Driving rain in the second half made conditions increasingly difficult, but it was Forest who looked the most likely.
Holt saw a header tipped over by Danby on the hour mark and Julian Bennett shot wide with a volley.
At the other end, Yeo curled an effort that Smith easily saved.
Forest substitute Junior Agogo had the ball in the net after unnecessarily touching Matt Thornhill's goalbound shot into the net just three yards from goal while in an offside position.
Late on Holt won a spot-kick after being brought down by Danby, but the keeper saved the resulting effort with his legs after diving the wrong way.
The best chance of extra-time fell to Agogo who rounded Danby but was denied by a goalline clearance from Laurence Wilson.