Both sides were shocking in front of goal as they played to a goalless draw on a rainy night in Johannesburg.
The result sees Wits up to third on the table with 45 points from 26 matches, one point above fourth placed Orlando Pirates while Chippa are in 13th place with 29 points, six points outside of the relegation zone.
Wits dominated proceedings for the large part, but their finishing in front of goal was poor and as a result they shared the spoils with the Chilli Boys.
The home side started positively with the first shot on goal in the second minute courtesy of Ben Motshwari, but his effort sailed wide.
In the 14th minute some good wing play saw Wits work a ball into the box for Henrico Botes to meet, but his header was superbly stopped by the keeper.
In the 30th minute Sibusiso Vilakazi had a shot on goal, but just like his teammates, he fired wide of goal from long range.
Chippa were virtually non-existent in the first half, but did manage a decent shot on goal in the closing seconds of the stanza when William Twala skimmed the wrong side of the upright from just inside the box.
Wits continued to dictate terms in the second half, but again their finishing was dreadful.
Calvin Kadi was guilty of missing a guilt edged chance in the 56th minute when he found himself in space on the edge of the box, but shot wide of the target.
In the end neither side could find the back of the net as the spoils were shared.