They didn't just try. They did and the ACLU fought for it because even though they suck they still had the right. Either way, if you think that there was some rise in neo-Nazi crap in Chicago you would be wrong as hell. You know it.
Actually the Nazis never marched in Skokie. The ACLU did fight and WIN against the laws that Skokie tried to put up to stop the march. But at the end of the day, the City of Chicago allowed Frank Collin (real name, Frank Cohn) his right to march in Marquette Park (which is nowhere near Skokie), which is where he wanted to have his demonstration all along.
About 10 people showed up for his march, all doing some weird Nazi cosplay. Then some of Collins' underlings outed him for kiddie porn and took their little hate group to North Carolina... Meanwhile, Collins changed his name again, moved to Wisconsin and started peddling weird new-Age theories about ancient civilizations