We present the prospects for the pre-merger detection and localization of binary neutron star mergers with third-generation gravitational-wave (GW) observatories. We consider a wide variety of GW networks that may be operating in the 2030s and beyond; these networks include up to two Cosmic Explorer (CE) sites, the Einstein Telescope (ET), 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 ET on its own is able to detect six and two sources per year at 5 and 30 minutes before merger, respectively, while providing a localization of <10 deg2. A single CE would detect but be unable to localize sources on its own. A two-detector CE 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 CEs and the ET would allow for <1 deg2 source localization at 5 minutes before merger for ∼seven 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.