We report on Chandra observations of the black widow pulsar, PSR B1957+20. Evidence for a binary-phase dependence of the X-ray emission from the pulsar is found with a deep observation. The binary-phase resolved spectral analysis reveals non-thermal X-ray emission of PSR B1957+20, confirming the results of previous studies. This suggests that the X-rays are mostly due to intra-binary shock emission which is strongest when the pulsar wind interacts with the ablated material from the companion star. The geometry of the peak emission is determined in our study. The marginal softening of the spectrum of the non-thermal X-ray tail may indicate that particles injected at the termination shock is dominated by synchrotron cooling.