Chester and Barnet failed to produce a goal but each gained a precious point in their efforts to avoid the drop.
Barnet will feel they should have taken all three points, with Chester keeper Chris MacKenzie particularly impressive when he denied Nicky Bailey one-on-one.
Chester's best chance came in the sixth minute when Jake Edwards volleyed over an open goal from just six yards out.
Late on Barnet had a decent penalty shout rejected, and also saw Tom Curtis clear the ball off Chester's line.
Chester: MacKenzie, Artell (Stephen Vaughan 45), Dimech, Hessey, Curtis, Drummond (El Kholti 26), Blundell, Davies, Regan, Edwards, Asamoah.
Subs Not Used: Harrison, Tait, Walker.
Booked: Dimech.
Barnet: Flitney, Hendon, Warhurst, Clist, King, Fuller, Kandol, Hessenthaler, Sinclair, Bailey, Hatch (Strevens 90).
Subs Not Used: Reed, Roache, Vernazza, Gross.
Booked: Warhurst.
Att: 2,367
Ref: M Pike (Cumbria).