The only bird in the USA that is not a protected species is the Common Crow. Shooting any other species of bird is a violation of federal and probably your state laws, and surprisingly Starlings are included in the protected species even though they are not native birds. If you are in an urban area discharging a firearm may also be illegal. Maybe you could get a special license to control these pigeons, but that is not too likely and would be very costly anyway.
Look around for deterents to their roosting.

I don't know if a pellet gun would be an effective way of controlling them, but -

"Pigeon, European Starling, or House Sparrow:
A permit is not required to kill or remove these species. The Migratory Bird Treaty Act (MBTA) does not protect these three species since they are not native to North America." uiuc.edu

Your state does not prohibit killing pigeons, if you are within Chicago city limits you might want to make a call to be sure you are within your homeowners rights.

Here is a link that might be useful: University Illinois Extension

theedudenator,

If you do decide to go the pellet gun route, you will want an accurate one, because birds are relatively small targets.

The Air Arms TX200 MkIII by Air Arms is well thought of and has a lot of favorable reviews. There are, of course, other good air guns that cost less, and some cost more. In any case, you should comply with all local, state, and federal laws.

ZM

My dad was one of those people that if you shot it you ate it. Bird for Sunday dinner:))

Too late for this year, but a nest box for owls may help.

tj

You can try "Bird Spider"

The Bird Spider 8'

4-Foot Bird Spider

http://www.gemplers.com/roosting-bird-repell

We had a serious problem with crows and the starlings that come with them (sort of like little jackels following their larger black buddies). They would wipe out all our fruit trees by only taking one peck out of each, then tearing off new growth. We tried everything for years (owl dummies, old CDs hanging, bird netting the smaller trees). Nothing worked. Then three years ago we bought some outdoor speakers, ran the wire to our house where we hooked up a MP3 selection (on our computer) of various song birds and various hawk sound bytes and play it early in the morning and occasionally during the day when those black winged gangsters start their fly by. We have never lost any fruit since playing those bird songs and osprey/hawk calls. The good thing is the neighbours don't complain about it as it sounds like a garden full of song birds most of the time. Seems that crows and especially starlings do not like to come around where there is a large active bird population. This year we sacrificed our small orchard to see if NOT playing the sounds had any change. Needless to say, we lost all our cherries, plums, crab apples and much of our new growth on most of our trees. So playing bird sounds really works for us at least. A much more natural and safer alternative to gun warfare.

I hadn't thought about that. Thanks for the tip! Bird netting is fine if the frame is big enough that the birds' beaks can't reach the plants through the mesh. I have one bird scare (not mine originally) that looks kind of like a colorful snake floating in the air (it hangs from a thin line). It may be working, or it may be that the place where it hangs isn't easily accessible or attractive to birds.