Arrows enjoyed an encouraging start to the encounter, with Kudakwashe Mahachi going close with a couple efforts in the opening 15 minutes.
The Chilli Boys had a chance to break the deadlock after 25 minutes but Moeketsi Sekola blazed over the crossbar from close range, following a well-worked move.
Chippa had most of the possession in the first half, but they were struggling to carve out clear-cut openings.
The next chance arrived just before the halftime when Lerato Lamola was denied by Daniel Akpeyi from close range.
Nevertheless, the score remained goalless as the sides entered the halftime break.
Chippa eventually broke the deadlock in the 58th minute courtesy of a strike from veteran forward Katlego Mashego.
Arrows managed to level matters in the 65th minute when substitute Knox Mutizwa headed past Akpeyi.
Teboho Moloi responded with a change 10 minutes later as Mashego was withdrawn for former Orlando Pirates winger Mahlatsi Makudubela.
Both clubs upped the tempo and pushed for a winning goal in the closing stages of the half.
However, Arrows and Chippa were forced to settle for a point after neither could carve out a clear-cut chance.