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.
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