This paper introduces a design of a gammatone filter based on stochastic computation for area-efficient hardware. The gammatone filter well expresses the performance of human auditory peripheral mechanism and has a potential of improving advanced speech communications systems, especially hearing assisting devices and noise robust speech recognition systems. Using stochastic computation, a power-and-area hungry multiplier used in a digital filter is replaced by a simple logic gate, leading to area-efficient hardware. However, a straightforward implementation of the stochastic gammatone filter suffers from significantly low accuracy in computation, which results in a low dynamic range (a ratio of the maximum to minimum magnitude) due to a small value of a filter gain. To improve the computational accuracy, gain-balancing techniques are presented that represent the original gain as the product of multiple larger gains introduced at the second-order sections. As a result, the proposed techniques maintain the original gain of the filter while improving the computational accuracy. The proposed stochastic gammatone filters are designed and evaluated using MATLAB that achieves a high dynamic range of 71.71 dB compared with a low dynamic range of 5.47 dB in the straightforward implementation.