For me (developing on windows 8, samsung S4 connected via USB ) chrome://inspect works, but only if I have adb running in the background. This was not mentioned in the documentation last time I checked.
Get android platform tools if you don't already have it. Then, from a command prompt in android-sdk/platform-tools > adb start-server.
You can do this as often as you like, and may need to do it every time you reconnect your phone, or wake your machine.