The bluetooth chip and antenna (I had to remove a metal shield to reveal the chip;)

The bluetooth chip, in this case the nRF51822 Nordic Semiconductors (It’s a 2.4GHz ultra low-power bluetooth chip built around a 32-bit ARM® Cortex™ M0 CPU)

To the right of the nRF51822, you can see two oscillators, one 16MHz and one 32.768kHz (marked in orange), which generate the clock waveforms for the CPU

On the bottom (marked in yellow) you see the antenna circuitry and the PCB antenna itself. As you can see, they did not use a balun chip, but instead created a matching network using some capacitors and inductors.