dIM Chat on the App Store!
What it is
dIM is a decentralized instant messenger (thus the name) which sends messages trough Bluetooth. It does not need an internet connection to send messages, which is what makes it special.
How it works
When you are in the range of another person who has dIM installed on their iPhone messages are relayed until they reach their destination. The range of Bluetooth Low Energy is officially 100m (330ft), but according to my tests the range is more like 80m (260ft).
See dIM chat for more information, the source code and documentation of the project.