There's no OOB widget available for the Connect Support application to be added to the Service Portal.
All releases pre-London
Pre-London releases it's expected behavior that there's no OOB widget for Connect Support. Instead Connect Support on the portal is controlled by the "Chat Queue" field on the Portal (sp_portal) record itself.
Enable Connect Support on the portal by adding in the "Chat Queue" field on a portal (sp_portal) record and populate it with a valid chat queue.
Once this is added the "Live Chat" link will be visible on the portal header for users to click onto and initiate the chat.
Please visit KB0683377 for more details regarding this.
Alternately a custom HTML or Icon widget for example can be created and the chat link can be coded into it. The chat link has the format of:
Starting in London release there is now a Connect Support widget that can be added to any pages in Service Portal. More information can be found on this documentation: