please list the best and top one that are well known and also produce the best of works thanks.
Check out the Old Town School of Folk Music…I doubt they have belly dancing, but I'm sure they have some type of vocal training. http://www.oldtownschool.org/ I'm sure they can at least point you in the right direction.
Other than that, I would suggest Googling "Belly Dancing School, Chicago" and then look up the results at http://www.chicago.metromix.com or http://www.chicago.citysearch.com