How to make iPhone camera silent?
A simple solution is to use the mute switch on the side of the phone.  The camera shutter sound is controlled by the ringer volume, since the mute switch mutes the ringer the shutter sound is also mute.  However, you are asking an optional permanent solution.  So far there is none.  The application doesn't have any additional options within the app or within System Preferences.

Digging into the app store there is a simple camera application called Secret Camera - Taking Photo Secretly for $1.99. Apple Store Link It looks like it functions like the normal Camera application, but reading its description it doesn't explicitly mention a shutter mute option.  I assume this is an implied feature due to the app's name.