Hey Nicolas: Here's where I recommend you start.
1. Connect with a local architect who specializes in new construction duplexes and get their feedback on the highest and best use of the land, as is. Since your lot is already zoned RS3, you can (by right) build a new SFH or 2-flat. You most likely won't need to rezone, or get a variance of any sort, unless your lot is shaped strangely. (eg, if your lot is not the standard 25 x 125, but some other multiple where the width is actually skinnier than 25, and the lenghth is longer than 125, and you want to reduce side setback requirements, eg.)
Additional Resources to check, 'FYIs', in case you want to learn more about rezoning in the future)
-Look up your address on the city's zoning map here to see how properties in your immediate vicinity are zoned. If you see at least a few zoned in the designations you mentioned above, that's potentially a good sign that you can get support from the local Alderman's office, and approval by the ZBA (zoning board of appeals), to rezone.
-Reach out to your Alderman's office. Speak with the director of development (they're not always titled that way, so just ask for whoever deals with area developments, new construction, rezoning, etc.) to ask if they'd be supportive of your plan. Your plan can be something rough like: I own a piece of vacant land at (address), and I'm looking to rezone it from (current designation) to (new designation) in order to build a new construction duplex which will consist of 2 condos for sale, or 2 aparment rentals, eg. Is that something the Alderman would be supportive of? *Again, this doesn't seem necessary on your current lot because you are allowed to build a 2-flat, by right, on RS3 land of that size.
-If it's determined that your Alderman would be supportive of your 'plan', and you've already connected with a local architect, you'll then want to reach out to a zoning attorney. Your architect can recommend someone they like or find your own.
*Note you do not need a zoning attorney, but I highly recommend you work with one.
*Also note that Aldermanic support is not required for a zoning change approval by ZBA. But I strongly urge anyone to always get Aldermanic support before proceeding because it makes life--and the entire project / process--a whole lot easier. :)
IN SUM: Based on what you've shared, it sounds like you won't need to rezone if you just want to build a duplex. Check with an architect first to be sure you can fit your vision into the existing lot, as it's zoned currently. If not, then the path of least resistance is to simply adjust your vision so it fits better into the lot, as-is. :) A zoning change can take up to 6 months, approval isn't guaranteed (despite Aldermanic support), and potentially cost a lot of money (architectural site / floor plans & dimensioned elevations, zoning attorney, holding costs, etc.)
Hope this helps. We're here if you have any other questions or would like to consider working with a design-build GC on your project. We specialize in new construction SFHs and small multi unit buildings in Chicago. Good luck!
Jennie Berger