Shrewsbury Town and Chester City both had chances but neither could break the deadlock in a poor game at New Meadow.
City, who still need a point to be safe from the drop, hit the post through Paul McManus after eight minutes.
Chris Humphrey came the closest to a goal from Shrewsbury with a strike that John Danby tipped round the post.
Guy Madjo failed to connect with a decisive touch for the Shrews as the ball rolled along the line while Ben Davies had a shot easily saved.
Shrewsbury: Bevan, Herd, Kempson, Murdock (Leslie 63), Tierney, Humphrey, Darren Moss (Hall 55), McIntyre, Davies, Hibbert (Constable 63), Madjo. Subs Not Used: Garner, Pugh.
Chester: Danby, James Vaughan, Kelly, Linwood, Wilson, Partridge, Sandwith, Roberts, Ellison (Rutherford 39), Murphy, McManus (Hughes 81). Subs Not Used: Palethorpe, Grant, Rule.
Booked: Ellison, Sandwith.
Att: 6,417
Ref: Rob Styles (Hampshire).
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