Blind multichannel identification is generally sensitive to background noise. Although there have been some efforts in the literature devoted to improving the robustness of blind multichannel identification with respect to noise, most of those works assume that the noise is Gaussian distributed, which is often not valid in real room acoustic environments. This paper deals with the more practical scenario where the noise is not Gaussian. To improve the robustness of blind multichannel identification to non-Gaussian noise, a robust normalized multichannel frequency-domain least-mean M-estimate algorithm is developed. Unlike the traditional approaches that use the squared error as the cost function, the proposed algorithm uses an M-estimator to form the cost function, which is shown to be immune to non-Gaussian noise with a symmetric α-stable distribution. Experiments based on the identification of a single-input/multiple-output acoustic system demonstrate the robustness of the proposed algorithm.