As the comments mention, you generally do not deploy files randomly in SharePoint as there is a specific structure that SharePoint expects at the root of a site. If you must do something like this, you might want to move it to a subdomain outside of SharePoint like chat.domain.com where domain.com points to sharePoint and chat.domain.com points to a regular IIS website that hosts the chat application. You could then add links/iframes in SharePoint to call the chat application.
From the Visual Studio side, you would treat it as a normal web application project.
HttpRuntime.AppDomainAppPath