Other threads on this topic have included http://giftedissues.davidsongifted.org/BB/ubbthreads.php/topics/36728/1.html
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While each list has a disclaimer stating essentially that the list is a courtesy, not an endorsement... known lists are:
- NAGC, and its state allifiates
- SENG
- Hoagies gifted education page (link- http://www.hoagiesgifted.org/psychologists.htm)

To learn more about a particular office or individual you may wish to use a search engine. For example, there may be youtube video interviews, blog posts, etc which may help families assess a comfortable "fit".
The NAGC affiliate for the Chicago area would be the Illinois Association for Gifted Children (IAGC) http://www.iagcgifted.org/

Here is an article on questions to ask a tester: http://www.davidsongifted.org/db/Articles_id_10112.aspx