The visitors should have opened the scoring inside the first 60 seconds, but Peniket blazed over the crossbar from 12 yards when it seemed easier to score.
Halifax continued to have the upper hand throughout the first 15 minutes and they thought that they had taken the lead through Scott Boden, but his effort was ruled out because of a foul.
Chester were very much on the back foot with Halifax's Jamie Jackson having a well-struck shot kept out and, 10 minutes before the break, the visitors finally took the lead.
Peniket received the ball 20 yards from goal before he curled the ball into the corner, out of the reach of Freddie Hall.
The hosts finally offered a threat in the final third during the closing stages of the half, but Peter Winn saw his shot deflected wide of the target.