Is it illegal to go for a walk during the quarantine in Chicago?

There is a stay at home order for the state of Illinois. You are allowed to go out, but keep a distance between others. Parks are closed.

There is NO QUARANTINE in Chicago.

Due to the Coronavirus, the city has restrictions on using lakeshore trails, but you can walk on any common public sidewalk.

Nobody is quarantined yet in the US, although Trump is talking about it for New York. The usual phrase is "Shelter at Home". Whether you can go for a walk depends on whether you can avoid contact with people and with surfaces that people have touched. You can't get it by walking outside- and there's some indication that warm weather and sunshine slow down the spread of the virus.