The solar wind has been extensively studied recently with in situ observations, and the understanding of its counterpart near the solar surface has also progressed significantly. With the spectroscopic observations from the Chinese Hα Solar Explorer (CHASE), the chromospheric Dopplergram of the full solar disk is first obtained almost simultaneously. By investigating the statistics of the Doppler velocities at the chromosphere, we find that the coronal hole (CH) regions are dominated by Doppler blueshifts, with a stronger net magnetic flux region corresponding to smaller blueshift velocity. In addition to the average blueshift, the probability density of the Doppler shift is not symmetrically distributed but shows an excess at the redshift side, while the reference region does not show such an asymmetry. The redshift asymmetry may provide a possible clue for the interchange reconnection that might happen just above the chromosphere. By sampling the regions at the network boundaries in the CHs, the probability density is slightly enhanced at the parts of both larger blueshifts and redshifts compared with the result for the whole CH region. As the reference region also shows such enhancement, the crucial area associated with the origin of solar wind is not identified efficiently by sampling the overall network boundaries as demonstrated here. The present study shows the first attempt at interpreting the origin of solar wind in the transient CHs based on the CHASE spectroscopic observations, and a combination of full-disk and high-resolution observations is helpful in the future for firmly understanding the source region of solar wind.