Feeding raccoons is not a good practice for several reasons. First, raccoons can carry canine distemper, rabies, roundworms, tapeworms and other viruses that can be fatal to humans. Second, it attracts more raccoons to an area than would normally be supported by local food resources, and it puts the animals in close contact with each other. This can cause the spread of disease between the raccoons. First, share this information with your neighbor if you can. Sometimes people aren't aware that they could be causing more harm than good.
If they refuse to stop feeding the raccoons, you can call Animal Control, explain the situation, and request that they pick up the animals to be euthanized (they may provide you with live traps and ask you to trap the animals which they will then pick up. It works differently in different communities. So you'll need to see what the procedures are in your local office). Other options would be to call the Illinois Department of Natural Resources district wildlife biologist. Or to hire a nuisance wildlife control operator to remove and euthanize the raccoons. You can find contact information for the IDNR biologist at: http://web.extension.illinois.edu/wildlife/professionals.cfm
