Go is a hosted, SaaS service that enables small and emerging merchants to quickly build and launch an online store. Since it is a hosted solution, you have no access to the physical files of it and you can't use the Live Agent - Magento plugin
into your shop.
First of all, you have to log in to the admin panel of your Magento Go store (e.g. myexamplesite.gostorego.com/admin ).
Then you have to navigate to System > Configuration > General > Design > Footer and there you scroll down to
Into that Miscellaneous HTML
window place the integration code of a chat
button that you obtained in Live Agent
Do not forget to click the Save Config button in the top-right corner of the particular screen.