  We present a study of NGC 4993, the host galaxy of the GW170817 gravitational
wave event, the GRB170817A short gamma-ray burst (sGRB) and the AT2017gfo
kilonova. We use Dark Energy Camera imaging, AAT spectra and publicly available
data, relating our findings to binary neutron star (BNS) formation scenarios
and merger delay timescales. NGC4993 is a nearby (40 Mpc) early-type galaxy,
with $i$-band S\'ersic index $n=4.0$ and low asymmetry ($A=0.04\pm 0.01$).
These properties are unusual for sGRB hosts. However, NGC4993 presents
shell-like structures and dust lanes indicative of a recent galaxy merger, with
the optical transient located close to a shell. We constrain the star formation
history (SFH) of the galaxy assuming that the galaxy merger produced a star
formation burst, but find little to no on-going star formation in either
spatially-resolved broadband SED or spectral fitting. We use the best-fit SFH
to estimate the BNS merger rate in this type of galaxy, as $R_{NSM}^{gal}=
5.7^{+0.57}_{-3.3} \times 10^{-6} {\rm yr}^{-1}$. If star formation is the only
considered BNS formation scenario, the expected number of BNS mergers from
early-type galaxies detectable with LIGO during its first two observing seasons
is $0.038^{+0.004}_{-0.022}$, as opposed to $\sim 0.5$ from all galaxy types.
Hypothesizing that the binary system formed due to dynamical interactions
during the galaxy merger, the subsequent time elapsed can constrain the delay
time of the BNS coalescence. By using velocity dispersion estimates and the
position of the shells, we find that the galaxy merger occurred $t_{\rm
mer}\lesssim 200~{\rm Myr}$ prior to the BNS coalescence.
