The following Nginx configuration enables CORS, with support for preflight requests.

# NOTE: Wide-open CORS config for nginx
location / {
     if ($request_method = 'OPTIONS') {
        add_header 'Access-Control-Allow-Origin' '*';
        add_header 'Access-Control-Allow-Methods' 'GET, POST, OPTIONS';
        # NOTE: Custom headers and headers various browsers *should* be OK with but aren't
        add_header 'Access-Control-Allow-Headers' 'DNT,User-Agent,X-Requested-With,If-Modified-Since,Cache-Control,Content-Type,Range';
        # NOTE: Tell client that this pre-flight info is valid for 20 days
        add_header 'Access-Control-Max-Age' 1728000;
        add_header 'Content-Type' 'text/plain; charset=utf-8';
        add_header 'Content-Length' 0;
        return 204;
     }
     if ($request_method = 'POST') {
        add_header 'Access-Control-Allow-Origin' '*' always;
        add_header 'Access-Control-Allow-Methods' 'GET, POST, OPTIONS' always;
        add_header 'Access-Control-Allow-Headers' 'DNT,User-Agent,X-Requested-With,If-Modified-Since,Cache-Control,Content-Type,Range' always;
        add_header 'Access-Control-Expose-Headers' 'Content-Length,Content-Range' always;
     }
     if ($request_method = 'GET') {
        add_header 'Access-Control-Allow-Origin' '*' always;
        add_header 'Access-Control-Allow-Methods' 'GET, POST, OPTIONS' always;
        add_header 'Access-Control-Allow-Headers' 'DNT,User-Agent,X-Requested-With,If-Modified-Since,Cache-Control,Content-Type,Range' always;
        add_header 'Access-Control-Expose-Headers' 'Content-Length,Content-Range' always;
     }
}