It's an open run. However, it is expected to run for about 18 months. According to Chris Jones of the Chicago Tribune on Dec. 9, 2015:
"From the producers' point of view, the ideal length of a Chicago run is not merely dependent on whether or not the show is selling out here. Rather, the issue is how much tickets are selling for. It is crucial to maintain scarcity of supply and to avoid discounting, a practice that not only cuts into profits but can undermine the ability of the Broadway production to command its stratospheric prices in New York. These days, conventional wisdom has it that you leave a city while demand for tickets still is sky high — and go to another city where you can be another box office sensation. The producers will not let demand in Chicago slow even a smidgen — and remember the venue in Chicago has about 500 more seats than the Richard Rodgers Theatre, where it continues to play."
After about a year, as the show ages and the tour(s) reduce the demand from regional tourists in the city, ticket buyers from the Chicago area would expect a normalization of the prices, particularly the premium prices. But as Chris Jones notes in the above article, the producers don't want to normalize the ticket prices, they want them to remain astronomical. Though Hamilton is a sold-out smash, it's demand appears to be more comparable to Wicked and the original tours of Phantom and Les Miz than it is to the outrageousness of the demand of its own Broadway production (which I attribute significantly to the scalpers and not so much the show itself).