No, SKS rifles are not legal in Chicago. Basically, no semi-auto rifles that have ever been used in combat (or their clones). No SKS, AK, AR, M1A, M1 Carbine, etc. Ironic that you can't own an M1 Garand but you can own a Remington 7400. Yeah, there's no rhyme or reason. A pump shotgun would be probably be the best bet. If he/she has their heart set on a semi-auto, you might go with a Marlin Camp Carbine, Ruger PC9 or something similar. A lever-action in a pistol caliber is a handy option, too, that's not so "scary."
Be sure they know that a Firearm Owner ID (FOID) card is required, gun transfers must go through an FFL and firearms must be registered annually in Chicago. Yes, it's a pain.