I have resolved this issue, but I don't know what was causing it. I tried using DebugDiag to take a dump and analyze it. The analysis indicated that the process was waiting for something to complete in a Compatibility module in some Microsoft code.
I noticed that there were two Compatibility Databases installed with IIS 8. I uninstalled both items and tried running my app again. This time the app successfully executed the line that was hanging.
While this resolved the issue on this machine, I still don't know what is causing the problem. I have a colleague with a similar configuration and he has no problem with the app hanging on the line above, even with the Compatibility databases installed.