Millimeter wave (mmWave) multiple-input multiple-output (MIMO) transceivers employ narrow beams to obtain a large array-gain, rendering them sensitive to changes in the angles of arrival and departure of the paths. Since the singular vectors that span the channel subspace are used to design the precoder and combiner, we propose a method to track the receiver-side channel subspace during data transmission using a separate radio frequency (RF) chain dedicated for channel tracking. Under certain conditions on the transmit precoder, we show that the receiver-side channel subspace can be estimated during data transmission without knowing the structure of the precoder or the transmitted data. The performance of the proposed method is evaluated through simulations.