Chiefs played most of the match with 10 men after Reneilwe Letsholonyane was shown a red card, while the game was also held up after a fan ran onto the field to confront referee Lwandile Mfiki.
Chiefs thought they had scored in the eighth minute, but Lehlohonolo Majoro was ruled offside. Two minutes later Chiefs keeper Khune was forced to make a good save after Tshepo Liphoko unleashed a brilliant shot from 18-yards out.
Majoro had another chance just before the half-hour mark when he found himself one-on-one with the keeper, but he shot wide.
The game then turned on its head when Letsholonyane was shown a red carded for a late challenge on Liphoko. Chiefs players and the bench protested the decision, before the fan made his way onto the pitch and tried to hit Mfiki with a vuvuzela.
Liphoko had another great opportunity late in the game when he received the ball on the left and fired a shot at Khune, but it went across the face of goal.
Two minutes later Chiefs got a break with Majoro setting up Siboniso Gaxa, but he lobbed his effort over the bar, before Siphiwe Tshabalala hit the side-netting with the last kick of the game.
There was more drama after the final whistle when Chiefs coach Stuart Baxter refused to shake Arrows counterpart Manqoba Mngqithi’s hand, with the latter saying: “I wanted to shake hand but he didn't want to, he can go to hell.”