We have used high-resolution spectra of the Ca II H resonance line in late-type dwarfs, obtained with high S:N ratios, over a period of four years to widen our understanding of the dynamical behavior of the Ca II emission cores. All of the stars dealt with in this article, which are chromospherically active, show variability both in core emission flux and line width. They also show significant wavelength shifts with time of order hundreds of meters per second in the mean core wavelength, and with lower amplitude in the H3 self-absorption, compared to the photospheric rest wavelength of Ca II H. Comparing the emission core shifts with those observed in the H3 features, we find, for the first time, direct prima facie evidence for vertical chromospheric velocity fields, which show stability in sense over periods of years in a given star, with notable modulation in gradient, and which differ in gradient from star to star. We present evidence to show that the observed effects are almost certainly not due to projected rotational modulation, and offer new prospects, given spectral measurements closely sampled in time, for investigating the vertical velocity structures of chromospheres.