We investigate the velocity field of the solar chromosphere at the location of 65 He i 10830 dark points (DP's). We have obtained spectra of such points in the vicinity of the Ca II K line. As a measure of differential chromospheric velocity, we use the shift of the K line center relative to a nearby photospheric Fe i line. We find that in He i DP's, the distribution of K line shifts is skewed towards the blue: the blueward skewing is more pronounced in He i DP's located in coronal holes. To the extent that He i DP's are proxies of coronal bright points, our study is relevant to previous reports of outflows from such bright points.
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