  Previous studies have shown that the large, diffuse galaxies NGC1052-DF2 and
NGC1052-DF4 both have populations of unusually luminous globular clusters as
well as a very low dark matter content. Here we present newly-obtained deep
Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS) imaging of one
of these galaxies, NGC1052-DF4. We use these data to measure the distance of
the galaxy from the location of the tip of the red giant branch (TRGB). We find
a rapid increase in the number of detected stars fainter than $m_{F814W} \sim
27.3$, which we identify as the onset of the red giant branch. Using a forward
modeling approach that takes the photometric uncertainties into account, we
find a TRGB magnitude of $m_{F814W,\rm TRGB}=27.47 \pm 0.16$. The inferred
distance, including the uncertainty in the absolute calibration, is $D_{\rm
TRGB}=20.0 \pm 1.6$ Mpc. The TRGB distance of NGC1052-DF4 is consistent with
the previously-determined surface brightness fluctuation distance of $D_{\rm
SBF}=18.7\pm 1.7$ Mpc to NGC1052-DF2 and is consistent with the distance of the
bright elliptical galaxy NGC1052. We conclude that the unusual properties of
these galaxies cannot be explained by distance errors.
