The draw is a blow to Chiefs' title chances, while Pirates extend their winless run to 11 games.
Chiefs had the lead in the first half through Joseph Molangoane, before Thembinkosi Lorch forced Tsepo Masilela into an own goal.
Willard Katsande had a golden chance to win it for Chiefs, but a poor penalty take saw his effort saved by Brighton Mhlongo.
It was a first Derby for new Pirates coach Kjell Jonevret, who made a big decision to select Thamsanqa Gabuza over top-scorer Tendai Ndoro up front.
Pirates started the brighter and could have been 2-0 up inside the first 15 minutes, with Itumeleng Khune making a magnificent stop from Dove Wome.
Chiefs had offered little going forward, but a defence-splitting ball from Siphiwe Tshabalala found Bernard Parker in space and he laid a square-ball for Joseph Molongoane to tap home the opener.
Khune made another good stop from Gabuza, before Molangoane was denied a second by a fine save from Mhlongo in the Pirates goal.
Pirates continued to do the pressing and claimed a deserved equaliser on 33 minutes as Lorch managed to squeeze the ball across goal and the ball came off Masilela and went through the legs of Khune.
The pace of the game continued in the second half, but there were not the same clear-cut chances as we saw in the first.
Chiefs had a superb chance to win the game when Ayanda Gcaba was adjudged to have handled the ball in the box, but Katsande's penalty was saved by Mhlongo.
It was, perhaps, justice served though as Gcaba could do little about the ball striking his arm. Katsande's weak penalty down the middle was saved by the legs of the keeper.
Chiefs are three points behind league leaders Cape Town City, but have played five games more than Mamelodi Sundowns, who are three points behind them.
Coach Steve Komphela is still waiting for his first 90-minute victory over Orlando Pirates after six Soweto Derby attempts.