Hendrick Ekstein was restored to the Chiefs line-up, while Wiseman Meyiwa dropped to the bench.
Chiefs carved out the first real chance after 14 minutes. Siphiwe Tshabalala whipped a cross to the far post, but Gustavo Paez placed his strike wide of the upright.
Arrows were happy to sit back and allow Chiefs to dictate the encounter, as they did look threatening on the counter.
Despite enjoying most of the possession, the AmaKhosi struggled to carve out clear-cut chances and there were restricted to efforts from distance.
Steve Komphela made a change at the start of the second half, as Bongolethu Jayiya made way William Twala.
Chiefs managed to carve out a chance in the 57th minute as Tshabalala turned provider to play in Paez, however Dube popped up with a fine block to deny the striker from six-yards out.
Clinton Larsen opted for his change on 66 minutes as Knox Mutizwa was brought on in place of Mduduzo Sibiya.
Tshabalala was proving to be Chiefs' liveliest player on the park and he went close to handing Chiefs the lead after after 78 minutes but his header was saved by Gumede.
Jooste nearly gifted Arrows the lead with his first touch, but Daniel Cardoso produced superb block in the box.
Arrows did carve out a chance in stoppage time, but Mutizwa was thwarted by the on-rushing Khune.
The clash did end on a sour not after Khune was stretchered off the pitch after a collision with Mutizwa.
Nevertheless, the score remained 0-0 at the full-time whistle, as Arrows maintain their unbeaten start.