I assume you are running Craft on a multi-environment config with to different domains.
You are getting this error because modern browsers block cross-site requests, and the live-preview is probably trying to load the template from another domain.
You can tell your server to allow a cross-site requests by sending a CORS-header. This header is called Access-Control-Allow-Origin
.
.
Try adding this to your .htaccess file:
Header add Access-Control-Allow-Origin "http://example.com"
This will allow all requests coming from example.com. To be safe add the header for each domain you use:
Header add Access-Control-Allow-Origin "http://example1.com"
Header add Access-Control-Allow-Origin "http://example2.com"
Header add Access-Control-Allow-Origin "http://example3.com"
Note: You need mod_headers
activated. And if you know what you're doing, you could also set this up in: httpd.conf <VirtualHost>