Terminology nit: s/encrypted/secure/ - lots of systems that have encryption are pretty insecure.

As to the question, how about OTR+XMPP or Signal. Signal desktop is in beta. I don't think you need to worry about running the desktop Chrome extension on iOS since there's a native iOS app too?

I'll have to look into OTR+XMPP. I was hoping for something straightforward for non-technical folks to use as well. Any recommendations on clients?

What I meant by iOS/Chrome is that you currently can't setup the desktop (Chrome) app with an iOS device, it's Android only.

OTR has issues in instant messaging (if the messages arrive out-of-order you have to restart the session). Also, OTR's security is session based while Axolotl's is message based (Axolotl is an improvement on OTR that Signal uses).

We ssh into a box and run unix "talk" ...

More seriously, is there a reason for native? Just it's a fairly arbitrary request without more detail, since a network connection is needed anyway. eg. WhatsApp web client is good enough that it 'feels' native.

I'm very happy with Threema (even though there's no Desktop client yet), and I'd certainly never use Signal because it's backed by the US government: https://news.ycombinator.com/item?id=8106721

+1 for Threema. The servers are located in Switzerland, it's a good iOS citizen with a clean interface, and it offers some unique features (e.g., polling).

Signal now has a desktop version which runs with Google Chrome: https://whispersystems.org/blog/signal-desktop/

SpiderOak is currently developing "Semaphor"; an end-to-end, zero-knowledge collaboration platform with native clients on mobile and desktop: https://spideroak.com/solutions/semaphor

Signal?

What's wrong with Telegram?

No private chats for Windows/Linux.

I'd also recommend Telegram.

Whether or not secret (end-to-end encrypted) chats are implemented is up to the client's author.

Not having secret chats in Telegram Desktop was a decision of the author - https://github.com/telegramdesktop/tdesktop/issues/5

They work in cutegram (qt based client. OS X, Linux, Windows, OpenBSD, Arch AUR, etc) - http://aseman.co/en/products/cutegram/

They work in the pidgin plugin (which works on all of the platforms supported by Pidgin) - https://github.com/majn/telegram-purple#readme

They also work in telegram CLI (which many bots are based on) - https://github.com/vysheng/tg

self hosted IRC

Since OP mentioned mobile, which IRC client would you recommend on Android. Maintaining a persistent connection is battery draining. Weechat + https://www.glowing-bear.org is what I've been using but you don't get notifications that way.

iMessage has end-to-end encryption.

No mobile client (for Android or Windows Phone), no desktop client (for Windows or Linux).