Hi, Debbie. I would suggest researching at the District level. For example, where we are in Dist. 204, there's info on their website about their gifted program which applies to all schools in the district.
Here's a link to
Chicago Public Schools Regional Gifted Centers. It looks like the application deadline for some of these schools, like Edison Regional Gifted Center, have closed for 2009-10.
Unfortunately, we don't live in that specific area (we are in Far West 'burbs), so I can't provide any personal experience feedback with the schools surrounding Melrose Park. However, we have family in Elmhurst (near Melrose Park) and a quick search shows that
Dist. 205 has a gifted program in place.
There is also a lot of support & info here regarding home schooling, if that is a potential option for you.