Swallows will now turn their attention to the play-offs against University of Pretoria (Tuks) and Cape Town All Stars starting this weekend to save their Premier Soccer League (PSL) status.
Chiefs opened the scoring after 20 minutes from the header of Njabulo Ngcobo who beat Junaid Sait in the box to connect with a well-taken cross from Reeve Frosler.
Just after the half-hour, attacker Kamohelo Mahlatsi worked his way into the penalty box past Kearyn Baccus and Ngcobo but his close range shot went agonisingly wide of the target.
A few minutes later, Swallows launched another attacker into the Chiefs danger area but their skipper Lebohang Mokoena was denied by Bruce Bvuma who parried the ball away to safety.
On the stroke of halftime, Chiefs were lucky not to concede when Bvuma forgot the basics of goalkeeping by fumbling a shot by Dillan Solomons onto his upright.