  The historic detection of gravitational waves from a binary neutron star
merger (GW170817) and its electromagnetic counterpart led to the first accurate
(sub-arcsecond) localization of a gravitational-wave event. The transient was
found to be $\sim$10" from the nucleus of the S0 galaxy NGC 4993. We report
here the luminosity distance to this galaxy using two independent methods. (1)
Based on our MUSE/VLT measurement of the heliocentric redshift ($z_{\rm
helio}=0.009783\pm0.000023$) we infer the systemic recession velocity of the
NGC 4993 group of galaxies in the cosmic microwave background (CMB) frame to be
$v_{\rm CMB}=3231 \pm 53$ km s$^{-1}$. Using constrained cosmological
simulations we estimate the line-of-sight peculiar velocity to be $v_{\rm
pec}=307 \pm 230$ km s$^{-1}$, resulting in a cosmic velocity of $v_{\rm
cosmic}=2924 \pm 236$ km s$^{-1}$ ($z_{\rm cosmic}=0.00980\pm 0.00079$) and a
distance of $D_z=40.4\pm 3.4$ Mpc assuming a local Hubble constant of
$H_0=73.24\pm 1.74$ km s$^{-1}$ Mpc$^{-1}$. (2) Using Hubble Space Telescope
measurements of the effective radius (15.5" $\pm$ 1.5") and contained intensity
and MUSE/VLT measurements of the velocity dispersion, we place NGC 4993 on the
Fundamental Plane (FP) of E and S0 galaxies. Comparing to a frame of 10
clusters containing 226 galaxies, this yields a distance estimate of $D_{\rm
FP}=44.0\pm 7.5$ Mpc. The combined redshift and FP distance is $D_{\rm NGC
4993}= 41.0\pm 3.1$ Mpc. This 'electromagnetic' distance estimate is consistent
with the independent measurement of the distance to GW170817 as obtained from
the gravitational-wave signal ($D_{\rm GW}= 43.8^{+2.9}_{-6.9}$ Mpc) and
confirms that GW170817 occurred in NGC 4993.
