With the new LiveHelp Server plugin ver 3.6 you can easily enable the chat image in a static position.
Follow the next steps :
1. Enter to your WordPress admin area and go to the Section "Manage Domains" on the plugin panel.
2. Locate the column "Configure Widget" for a local widget or "Download Widget" for a external site and click.
3. On the general widget area you can select the "ActiveHelper LiveHelp" widget and deploy in a available area.
4. Deploy the widget and select the absolute position in order to display the chat image in a static position in your site.
5. You can test different statics positions, the widget includes 8 positions.
6. After you end click over the button "save" in order to keep the changes.
7. Go to your site and check the chat widget.