With Woopra it is possible to contact a visitor by chat. I like to propose a piwik-plugin equivalent to this.
With best regards Innocentus Keywords: outofscope
If someone actually writes such a plugin, we would gladly accept it as a 3rd party plugin, however this is not going to be part of Piwik core.
There are a few open source, live chat apps that we could integrate with, rather than embed.