They want a judge to strike down the law to allow them to be closer to the United Center.
If recent pro-Palestinian demonstrations are any indication of what could happen in August, when the DNC comes to Chicago, it could help explain the reasoning for restrictions the city has placed on where protesters can assemble.
A coalition of groups fighting that have now filed for a preliminary injunction, asking a federal judge to grant them better access.
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"Instead of meeting with us and working out a compromise that brings us within sight and sound of the DNC, the city has tried to shut us away in a corner," said Liz Rathburn with Students for a Democratic Society at the University of Illinois Chicago.
The groups want to hold their demonstrations close to the United Center, where the convention will be held, but have instead been told they are restricted to the stretch of Columbus Drive from Roosevelt to Jackson. That location is more than 3.5 miles away.
"Let us not fool ourselves. We are here today because the city of Chicago is working with the Democratic National Committee to avoid the image of protesters delivering political messages to the president of the United States," said Chris Williams, an attorney for Coalition to March on the DNC.
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Law professor Richard Kling, who took part in demonstrations during the 1968 convention, says the First Amendment doesn't guarantee people proximity to any location for their demonstrations.
"I appreciate the fact they would like to make it much closer to the convention. But there's all sorts of problems with respect to security and safety of the people in the convention and the rest of the community to continue to work," Kling said.
The next round in this fight will take place in federal court. But regardless of the outcome, enforcement of protest restrictions could end up being a challenge for police.
"I think the bottom line is protesters are gonna go where the protesters wanna go," Kling said.