We present the results of an experiment in which we observe a sub-Poissonian photocurrent. This photocurrent is generated by detecting the light emitted from a high-quantum-efficiency light-emitting diode driven by a high-impedance current source. We also present classical, semi-classical and quantum mechanical theories of photoelectric detection. The observed sub-Poissonian statistics are in agreement with quantum mechanical predictions, but are unexplainable using the classical and semi-classical theories. The experiment uses only equipment already found in most undergraduate laboratories, making this a nice experiment to demonstrate a purely quantum mechanical effect.