  The extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 14
sample includes 80,118 Luminous Red Galaxies. By combining these galaxies with
the high-redshift tail of the BOSS galaxy sample, we form a sample of LRGs at
an effective redshift $z=0.72$, covering an effective volume of 0.9~Gpc$^3$. We
introduce new techniques to account for spurious fluctuations caused by
targeting and by redshift failures which were validated on a set of mock
catalogs. This analysis is sufficient to provide a $2.6$\% measurement of
spherically averaged BAO, $D_V(z=0.72) = 2353^{+63}_{-61} (r_d/r_{d,\rm{fid}})
h^{-1}$Mpc, at 2.8$\sigma$ of significance. Together with the recent
quasar-based BAO measurement at $z=1.5$, and forthcoming Emission Line
Galaxy-based measurements, this measurement demonstrates that eBOSS is
fulfilling its remit of extending the range of redshifts covered by such
measurements, laying the ground work for forthcoming surveys such as the Dark
Energy Spectroscopic Survey and Euclid.
