In this paper the noise behavior of a novel Avalanche Ion Sensitive Field Effect Transistor (A-ISFET) is presented. The A-ISFET is an ion sensitive field effect transistor that can inherently deliver high sensitivity through a multiplication factor, M, similar to an avalanche photodiode, where they are used when the input signal is very weak. A physical model for both intrinsic and extrinsic noise mechanisms in an A-ISFET is derived. We developed an analytical model for the A-ISFET signal-to-noise ratio (SNR) to maximize SNR at a specific operating point, as a function of current components, noise sources and overall structure and operation. Based on our noise model, an optimum value for the multiplication gain is found to maximize SNR sensitivity of the A-ISFET sensor.