  The ultra-diffuse galaxy NGC1052-DF2 has a very low velocity dispersion,
indicating that it has little or no dark matter. Here we report the discovery
of a second galaxy in this class, residing in the same group. NGC1052-DF4
closely resembles NGC1052-DF2 in terms of its size, surface brightness, and
morphology; has a similar distance of $D=19.9\pm 2.8$ Mpc; and also has a
population of luminous globular clusters extending out to 7 kpc from the center
of the galaxy. Accurate radial velocities of the diffuse galaxy light and seven
of the globular clusters were obtained with the Low Resolution Imaging
Spectrograph on the Keck I telescope. The velocity of the diffuse light is
identical to the median velocity of the clusters, $v_{\rm sys}=\langle v_{\rm
gc} \rangle=1445$ km/s, and close to the central velocity of the NGC1052 group.
The rms spread of the observed velocities is very small at $\sigma_{\rm
obs}=5.8$ km/s. Taking observational uncertainties into account we determine an
intrinsic velocity dispersion of $\sigma_{\rm intr}=4.2^{+4.4}_{-2.2}$ km/s,
consistent with the expected value from the stars alone ($\sigma_{\rm
stars}\approx 7$ km/s) and lower than expected from a standard NFW halo
($\sigma_{\rm halo}\sim 30$ km/s). We conclude that NGC1052-DF2 is not an
isolated case but that a class of such objects exists. The origin of these
large, faint galaxies with an excess of luminous globular clusters and an
apparent lack of dark matter is, at present, not understood.
