Do I need to physically go to Chicago to get Visa stamp (for working/teaching 1 year? Or... Can I mail my passport and job offer letter with return stamped envelope?

You have to go personally to the Consulate but to be sure check their website to follow all the necessary steps you need to do. That would be my advise.

There are legal companies that will send someone that can stand in line for you like Erica L. said.

Unfortunately you can't mail it, but if you can't make it there you can work with some of the visa companies (you basically pay someone to go stand in line to turn in your visa info).