I now that chrome applications can deliver an experience close to that of native applications, but I could not find a way yet to run a local command from a chrome application. Is there any API for this that could used after the user has given permission? How can this be done?
Thanks
It is in principle possible via Native Messaging.
You can have a native app specifically designed to talk to your Chrome app, but the downside is that the native component cannot be bundled with the app in the Web Store. You'll have to use a separate installer.
Note that the above documentation is for extensions, but the corresponding calls are mentioned in the apps documentation as well.