A great increase in wireless access rates might be attainable by using the large amount of spectrum available in the millimeter wave (mmWave, 30 - 300 GHz) band. However, due to higher propagation losses inherent in these frequencies, to use wider bandwidth for transmission at ranges beyond 100 meters or in non-line-of-sight (NLOS) settings may be ineffective or even counterproductive when the penalty for estimating the channel is taken into account. In this work we quantify the maximum beneficial bandwidth for mmWave transmission in some typical deployment scenarios which use pilot-based channel estimation and assume a minimum mean square error (MMSE) channel estimator at the receiver. We find that for an I.I.D. block fading model with coherence time $T_c$ and coherence bandwidth $B_c$, for transmitters and receivers equipped with a single antenna, the optimal (rate-maximizing) signal-to-noise-ratio is a constant that only depends on the product $B_cT_c$, which measures the channel coherence and equals the average number of orthogonal symbols per each independent channel coefficient. That is, for fixed channel coherence, the optimal bandwidth scales linearly with the received signal power. Under some typical deployment scenarios with both transmit and receive side beamforming, 1 GHz bandwidth can be too much.