The VFSGlobal website mentions that they require 15 days processing time to get a Schengen visa through the Sweden consulate in Chicago. I was wondering if anyone had any experience where it took less. The earliest appointment I could get is in late May and my intended departure is exactly after 16 days.
I am writing down my experiences here: As I had mentioned in a previous comment, I had called VFS Global on their USA helpline to learn about any premium service with an extra fee if necessary. According to the representative who took my call the Chicago office did not offer any premium service; however, expedited service could be obtained only in case of a medical emergency. The situation may be different in other offices. A few days later I was lucky to find a vacant appointment slot on 15th May and promptly rescheduled my appointment. At the center I was told that every appointment needs to be at least 21 days before the scheduled departure (so my application would have been denied if I were stuck with the old appointment date). I took with me all documents and they took my passport. I got back my passport with visa after 16 days (12 business days). I could make the trip.