From now there is a way to get notifications about new chat request just by using skype. Here is requirements

• Installed sevabot
• Live Helper Chat with sevabot extension https://github.com/LiveHelperChat/livehelperchat-extensions/tree/master/sevabot

I won't talk there about sevabot install, you can find everything there http://sevabot-skype-bot.readthedocs.org/en/latest/ubuntu.html

As for configuring Live Helper Chat sevabot extension workflow is the following

1. Make sure you have running and working sevabot
2. edit extension settings file settings/settings.ini.php and set chat id and recipient id's, sevabot http url, and shared secret word
3. Chat id's you can find in sevabot http manager interface.

Also for testing purposes you can edit sevabot/modules/test.php

If you are afraid of sevabot installation complexity there is simple option to buy my prepared sevabot image snapshot on digitalocean. Read here for more information.

FAQ

What information is send as skype notification?

You will receive notification about new chat request with link to accept a chat. It will be enough just click link to accept and start a conversation with client.