  We present the prospects for the pre-merger detection and localization of
binary neutron star mergers with third generation gravitational-wave
observatories. We consider a wide variety of gravitational-wave networks which
may be operating in the 2030's and beyond; these networks include up to two
Cosmic Explorer sites, the Einstein Telescope, and continued observation with
the existing second generation ground-based detectors. For a fiducial local
merger rate of 300 Gpc$^{-3}$yr$^{-1}$, we find that the Einstein Telescope on
its own is able to detect 6 and 2 sources per year at 5 and 30 minutes before
merger, respectively, while providing a localization of $<10~\textrm{deg}^2$. A
single Cosmic Explorer would detect but be unable to localize sources on its
own. A two-detector Cosmic Explorer network, however, would detect 22 and 0.4
mergers per year using the same criteria. A full three-detector network with
the operation of dual Cosmic Explorers and the Einstein Telescope would allow
for $<1~\textrm{deg}^2$ source localization at 5 minutes before merger for
$\sim7$ sources per year. Given the dramatic increase in localization and
detection capabilities, third generation observatories will enable the regular
observation of the prompt emission of mergers by a broad array of observatories
including gamma-ray, x-ray, and optical telescopes. Moreover, sub-degree
localizations minutes before merger, combined with narrow-field-of-view
high-energy telescopes, could strongly constrain the high-energy pre-merger
emission models proposed in the last decade.
