Are you referring to the live agent URL that you are taken to when you click the "chat" button? If so, I do not believe you can customize this. I believe you may be able to recreate the chat experience using the REST API [1] but it's not a trivial thing to do.
[1] https://developer.salesforce.com/docs/atlas.en-us.198.0.live_agent_rest.meta/live_agent_rest/live_agent_rest_understanding_resources.htm