Signal Desktop is a free desktop app for secure one-to-one or group chats, with support for file attachments and media sharing.
The app is the desktop version of the iOS/Android app, Signal Private Messenger, although it only connects to Android systems right now.
You don't need to use both the Android and Chrome builds, but if you do, you'll find the two work well together. Open the desktop app and you'll find all the same conversations you've started on your mobile.
Wherever you're using it, Signal's major plus point is its security (the developer has even been endorsed by Edward Snowden). End-to-end encryption protects everything you're doing from snoopers, even Signal's server doesn't have access to your communications, and the app is open-source so technical users can review the code to check what's going on.
Signal doesn't even require any user names, passwords or PINs - you just use your existing phone number and address book (which is easy, but keep in mind it also gives your phone number to every chat partner).
There's plenty to do, but Signal's excellent security means it's already a good privacy choice.