Like most of you, I've always wanted want to code and compile 68k Mac OS applications in OS X that work on System 1.1. This question kept me up night after night, but thanks to Steven Troughton-Smith, we now know that it is, indeed, possible. It started with a 68k application on System 6. Not long after, he managed to compile a simple application that worked on System 1.1. This test application's code is available on github.
This is possible using ksherlock's MPW Emulator, which, as the name implies, is an emulator that allows you to run the Macintosh Programmer's Workshop on any OS X 10.9 system (a case-insensitive HFS+ volume is required).
I'm glad this matter has been settled. In all seriousness, while the number of useful applications for this is probably limited, it's still very cool.