I'm not finding a way to do this in the chrome.* API or even the experimental. It doesn't run through wscript so
ActiveXObject("Shell.Application")
isn't allowed.
I fear that my only option is to build a dll with NPAPI but I wanted to see if there was a simpler way.
To update this for a fellow wary lonesome traveler, even NPAPI is deprecated and being phased out. One of the alternatives mentioned in the NPAPI decprecation blog post that looks suitable for this type of problem (and pretty nifty really) is the Native Messaging API.