We propose a randomly-biased quadrature phase shift keying (QPSK) signaling scheme for a noncoherent Rayleigh block-fading multiple-input multiple-output (MIMO) channel. In order to optimize a prior of bias, we evaluate a lower bound of the spectral efficiency of the noncoherent MIMO channel with randomly-biased QPSK signaling in the large-system limit, by using the replica method. Our main result is that randomly-biased QPSK signaling with vanishing bias is optimal in the large-system limit for any signal-to-noise ratio.