The information transfer through a single neuron is a fundamental information processing in the brain. This paper studies the information-theoretic capacity of a single neuron by treating the neuron as a communication channel. Two different models are considered. The temporal coding model of a neuron as a communication channel assumes the output is ¿ where ¿ is a gamma-distributed random variable corresponding to the interspike interval, that is, the time it takes for the neuron to fire once. The rate coding model is similar; the output is the actual rate of firing over a fixed period of time. We prove that for both models, the capacity achieving distribution has only a finite number of probability mass points. This allows us to compute numerically the capacity of a neuron. Our capacity results are in a plausible range based on biological evidence to date.