Signal Private Messenger is a free app for secure one-to-one or group chats on mobile phones, avoiding SMS fees, and with support for file attachments and media sharing.
That's nothing unusual, but Signal's major plus point is its security. 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 to use, but keep in mind it also gives your phone number to every chat partner.)
The developer also warns that the Android version "is not currently compatible with tablets, but support for larger screens is on our roadmap and will be included in a future release".
There are better chat programs around, but Signal Private Messenger's core security is excellent, and the developer has even been endorsed by Edward Snowden and Bruce Schneier.