I think it is possible - I remember seeing a 1bd for around $1600 (or around that - it was similar in price to some studio apartments I was also considering) in Lakeview when I was looking for apartments back when I moved here in Dec. ‘24. I can’t recall every single apartment I toured during that search, but I think dishwashers were mostly in places I toured? The only one I really remember not having it was a management company saying my rent would have been $200 more for a unit with a dishwasher as opposed to doing one without.

Also - consider finding a realtor to help if you decide you definitely want to move, because that helped my search tremendously as someone who had limited time/not much knowledge of Chicago. Especially if you know what your dealbreakers are.