Swindon were awarded a penalty on 9 minutes after a hand ball in the box. Jack Smith took the kick to send the 'keeper the wrong way and give Swindon a 1-0 lead.
Swindon had plenty more chances to score with Chester's 'keeper having to make plenty of good saves to keep them in the game with the best chance falling to Blair Sturrock on the half hour mark where the 'keeper just tipped the ball around the post and out of a corner.
Jerel Ifil came close for Swindon in the second half from a header.
Chester rarely looked like scoring, so it was a quiet afternoon in goal for Phil Smith.
Overall an good win for Swindon, who should have scored 3 or 4 goals if it wasn't for the good game the Chester 'keeper had. The win now moves Swindon back up to 3rd place with a game in hand. Next weekend Swindon travel to Stockport where in the past few games at Stockport there have been plenty of goals.