BTLE
Arduino library for basic Bluetooth Low Energy support using the nRF24L01+ (basic support = sending & receiving on the advertising broadcast channel)
You will also need to install the RF24 library installable either from the Arduino IDE or https://github.com/TMRh20/RF24 .
Note: the BTLE class and the examples are licensed under GPLv3. However, the helper functions in btle.inc are (C) 2012 by Dmitry Grinberg under a separate license (see file for details).
FAQ
The nRF24L01+ can only send and receive up to 32 bytes. For advertising messages, this means 32 - 6 (MAC) - 2 (header) - 3 (CRC) = 21 bytes of payload can be sent and received at most. Consequently, a full iBeacon message won't fit in there and will never be received. Also, if you're sending advertisements from your phone, the device name alone will take up a significant chunk of that budget.