Due to known information processing capabilities of the brain, neurons are modeled at many different levels. Circuit theory is also often used to describe the function of neurons, especially in complex multi-compartment models, but when used for simple models, there is no subsequent biological justification of used parts. We propose a new single-compartment model of excitatory and inhibitory neuron, the capacitor-switch model of excitatory and inhibitory neuron, as an extension of the existing integrate-and-fire model, preserving the signal properties of more complex multi-compartment models. The correspondence to existing structures in the neuronal cell is then discussed for each part of the model. We demonstrate that a few such inter-connected model units are capable of acting as a chaotic oscillator dependent on fire patterns of the input signal providing a complex deterministic and specific response through the output signal. The well-known necessary conditions for constructing a chaotic oscillator are met for our presented model. The capacitor-switch model provides a biologically-plausible concept of chaotic oscillator based on neuronal cells.