Both sides played positively from the outset, although it was Chiefs, with Abia Nale and Simphiwe Tshabalala both in inspirational form, who fashioned the better opportunities.
Zito Ogbanna had the first chance of the game after just 20 seconds, but his shot from a tight angle was never going to bother Ajax keeper Andre Petim.
Kaizer Motaung Jnr had a far better chance in the 13th minute, but his parting shot from Arthur Zwane's cross was a tame effort.
For their part, Ajax threatened on numerous occasions down the wings, but Franklin Cale in particular disappointed with his final ball.
The home side were, however, presented with a great chance in the 22nd minute when SifisoVilakazi beat the offside trap, but he was unable to beat Chiefs keeper Emille Baron, who moved quickly off his line to make a block.
Eight minutes later Baron was again called into action to keep out a stinging drive from Sameehg Doutie.
This signalled a greater sense of urgency from the Cape Town side and Chiefs soon found themselves on the back foot, as Dipsy Selolwane came close with a rasping shot and then Doutie wasted a great opportunity when a weak touch prohibited him from profiting from Cale's superb delivery.
It was Chiefs though who had a great opportunity to draw first blood when a goalmouth scramble saw the ball falling to Onismor Bhasera right in front of goal, but the Zimbabwean made a real hash of his shot.
A minute before the half time whistle Craig Rosslee's men could also have gone in front when Joseph Masel burst into the box, but instead of trying to beat Baron from a tight angle, he picked out Vilakazi, whose subsequent shot was semi-blocked before it was cleared off the goal-line.
It was the Soweto giants who dictated play early in the second half, but Ajax were not unduly troubled as Chiefs failed to put their ball possession to good use.
Selolwane came close to opening proceedings in the 62nd minute but could not quite get on the end of Doutie's tantalising cross.
Ten minutes later Chiefs had their first chance of the second half when Reneilwe Letsholonyane picked up on a loose ball outside the box, but his effort was a couple of yards off target.
With a large portion of the Athlone crowd consisting of Chiefs fans, Motaung Jnr was handed the opportunity to become the hero of the day when a mistake by Eduardo Ferreira gave him a clean run on goal, but in trying to place the ball past Petim, he was unfortunate to see the ball striking the upright.
The most relieved player in the Ajax side was certainly defender Ferreira, whose careless mistake only a week ago a similar error gifted Swallows striker Shaun Haschick the winning goal.
Ajax mounted a late challenge with three successive corners, but the Amakhosi defence held firm as they ensured a point from a highly-entertaining game.