The blind multichannel identification is useful in many applications. Although many approaches have been proposed to address this challenging problem, the adaptive filtering-based methods are attractive due to their computational efficiency and good convergence property. The multichannel normalized least mean-square (MCNLMS) algorithm is easy to implement, but it converges very slowly for a correlated input. The multichannel affine projection algorithm (MCAPA) is thus proposed to speed up the convergence. However, the convergence of the MCNLMS and MCAPA is still unsatisfactory in practice. In this paper, we propose a time-domain Kalman filtering approach to the blind multichannel identification problem. Specifically, the proposed adaptive Kalman filter is based on the cross relation method and also uses more past input vectors to explore the decorrelation property. Simulation results indicate that the proposed method outperforms the MCNLMS and MCAPA significantly in terms of the initial convergence and tracking capability.