Chadwick secured the points for Chester with his 76th-minute goal
Bottom club Chester got their season off and running as they recorded their first Blue Square Premier win.
The Stutes almost took the lead when Nathaniel Knight-Percival's rasping left-foot drive struck the post.
Kevin Roberts headed City in front just before the break from Neil Ashton's corner after Danny Naisbitt had turned Nick Chadwick's effort round the post.
Chadwick then wrapped up the points 14 minutes from time against fellow strugglers Histon, heading the second.
Chester had lost their previous two home games and are now up to minus-20 points from six games.
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