Problem with TinyMCE button in Multisite

We're having a problem with the TinyMCE button for wordpress-chat in our multisite, tested with default themes + no other plugins. The chat plugin is activated on the child site, but not on the main site or the network. In a subfolder site (http://mywordpress.com/childsite), the TinyMCE button pops up a properly-formatted window with nothing but a zero in it.

Digging in, I found that the request is
GET https://mywordpress.com/wp-admin/admin-ajax.php?action=chatTinymceOptions
which is getting a response of 0 because that url should be
GET https://mywordpress.com/childsite/wp-admin/admin-ajax.php?action=chatTinymceOptions

The problematic code is in wordpress-chat/tinymce/editor_plugins.js::~line 18
file : url + "../../../../../wp-admin/admin-ajax.php?action=chatTinymceOptions",

Can you fix, please?

Thanks!