Here is the response I received from WordPress forums:
It appears to be that the list at Settings > Writing is for all the post formats. It is for choosing a default. But the list in the editor and in the Quick Edit and in the Bulk Edit are dependent on what the theme has for add_theme_support( ‘post-formats’, xxx).
There is this plugin: https://wordpress.org/plugins/bulk-convert-post-format/ which should work even though it is a little old.
But if you aren’t seeing the chat format in the list to choose from, your theme doesn’t support it, so it won’t look any different if you switch to it.
I installed the plug-in and it worked as chat post format was in the list. 🙂