Tom, you can manage messages mode settings in Admin Area > Plugins > Messages plugin settings. Change the messages mode displaying. But in this case the changes will be applied to the desktop and mobile version concurrently. If you want to change chat displaying just for mobile version this is considered as a custom code modification.
If you are not familiar with the code modification or plugin development, it would be better for you to find a developer who can help you. You can do it here: http://www.oxwall.org/market/specialists.
Also you can make a suggestion on uservoice: http://oxwall.uservoice.com/forums/13756-ideas-for-oxwall.

Yea, I just turned off the chat, not many people where using it and with the new theme on the phones it was wasted bandwidth for loading.

I would seriously consider putting an option in with the Cpannel. These responsive themes seem to be the answer to mobile and many may not want chat on their phones.

If you switch off the chat in admin. You will find that message functions (like on profile) will still open up a chat box, rather than a message box.

I was looking for a way to turn it off for mobile. But I got distracted. I guess it could get switched off via css, without hacking the plugin.

Oxwall has a bunch of options that would make life much easier for site owners - turning features on or off etc. Most of them, seem like easy wins for UX.

Matt, I've tried to reproduce this situation with opening a chat box rather than message box but have no success. Could you please provide more detailed steps how I can reproduce this on our Demo. And it would be really helpful if you attached some screenshots.