It is illegal to feed deer in Illinois, but not squirrels, chipmunks or raccoons. See the Illinois Department of Natural Resources guidance below. Some communities do have wildlife feeding ordinances, so you should check with Lake Zurich if they have such a policy.
As posted in the 2012-13 IDNR Hunting Digest:
"It is unlawful to make available food, salt, mineral blocks or other products for ingestion by wild deer or other wildlife in areas where wild deer are present. Except: - elevated bird/squirrel feeders providing seed, grain, fruit, worms or suet for birds or squirrels located within 100 feet of a dwelling devoted to human occupancy. - incidental feeding of wildlife within active livestock operations. - feeding of wild animals, other than wild deer, by hand as long as a reasonable attempt is made to clean up unconsumed food. - feeders for wildlife other than deer so long as deer are excluded from the feed in and around the feeder by fencing or other barriers. - standing crops planted and left standing as food plots for wildlife. - grain or other feed scattered or distributed solely as a result of normal agricultural, gardening or soil stabilization practices. - standing, flooded or manipulated natural vegetation or food/seed deposited by natural vegetation. - grain or other feed distributed or scattered solely as the result of manipulation of an agricultural crop or other feed on the land where grown, for purposes of dove hunting. - food material placed for capturing or killing wildlife pursuant to 520 ILCS 5/2.37, 2.30, and 1.3. - scientific permits issued pursuant to 17 Ill. Adm. Code 520 that allow food to attract wildlife. - any other permits issued by DNR that require the attraction of wildlife for purposes of management, research or control.
Violation of the provisions of this part is a Petty Offense with a maximum fine of $1,000".