Lopy12,
I found this info after doing a google search of municipal codes. I understand your frustration with the birds but it could get very expensive if you shoot any of them. It's not worth the risk. Maybe you should get a slingshot and a bag of small pebbles. You may feel better if you can at least scare them away. If you can get above them, from the roof, you can shoot down at them. That would be the safest way to keep whatever you are shooting on your property. Maybe an airsoft gun would work. I had one which I gave to my grand-nephew which I used to scare pigeons off my deck. I didn't kill any but the stopped crapping on my deck. I live in Illinois too, the gun laws suck. Good luck.
8-24-040 Discharging toy firearms; Replica air guns.
(a) Except as provided in subsection (c) below, no person shall at any time discharge or set off anywhere within the city, or have in his possession for such purpose any toy firearm, air rifle, toy cannon, or any gun, other than a replica air gun, that discharges projectiles either by air, spring, explosive, substance, or any other force.
(b) Except as provided in subsection (c) below, no person shall possess or discharge a replica air gun in the city of Chicago.
(c) The use or possession of an air gun or replica air gun is permitted if the air gun or replica air gun is in the possession and control of a carnival and is offered for use to carnival customers on a temporary basis. For purposes of this section, “carnival†means an enterprise which offers amusement or entertainment to the public by means of one or more amusement attractions or amusement rides.
(d) As used in this section, the term “replica air gun†shall be defined as provided in Section 4-144-145 of the code.
(e) Any person who violates the provisions of subsection (b) of this section, upon conviction thereof, shall be fined not less than $500.00 nor more than $1,000.00 for each offense, or imprisoned for a period not to exceed six months, or both such fine and imprisonment. As an alternative to, or in addition to, any such fine, the violator may be made to perform community service. Whenever a person under the age of 18 is ordered to pay a fine or perform community service for a violation of this subsection (b), the parent or guardian having legal custody or control of the person may be ordered to pay the fine instead of, or perform the community service in conjunction with, the person.