I haven't seen Hamilton in Chicago, but it is usually not a sell-out months in advance like the NY production. I just looked on Ticketmaster at a random date in June when Cher will be running concurrently, and there are several regular (i.e., non-resale) tickets available. They're still priced outrageously ($300-400; $147 for partial view), but they're there. I've even seen a significant number of orchestra seats priced down to non-premium prices, sometimes as low as $60-$80, for weekday matinees, but that might not be the case when summer gets here. There are seats to be had, though, depending on your price point. I'd recommend watching Ticketmaster periodically.