The realities of the browser environment make it impossible to do what you describe. It's been possible with native clients for a long time, but has always been pretty cumbersome for non-geeks--I've been working on a native client solution that would be easy for non-geeks to use and provide a few different levels of security (which come with varying levels of convenience) that are all better than the "plain-text everywhere" option most people use now.

I posted a link to this yesterday and don't mean to spam, but the topic has come up a few times in the past day, so: http://parley.co