The win saw Amakhosi extend their lead at the top of the log standings.
It was clear that Chiefs who were looking for an early goal as they took the game to Arrows early on, but the Abafana Bes’thende defence stood strong.
Chiefs appealed for a penalty in the sixth minute after the ball appeared to have hit the hand of an Arrows player, but the referee waved play on.
Erick Mathoho saw his shot hit the side netting in the 21st minute.
Arrows’ best chance fell to Siyabonga Dube in the 37th minute, but his shot on goals went over the crossbar.
The game remained 0-0 at the half-time break.
Chiefs continued to ask questions from the Arrows defence in the second half, but the Abafana Bes’thende remained resolute.
Lebogang Manyama finally broke the deadlock during the referee’s optional time when he capitalised on a rebound after the Arrows goal had parried away Samir Nurkovic’s shot.