The devastating impacts of extreme weather events, many of which are climate-change related, are increasingly evident through the frequency and duration of outages on power grids, especially the distribution systems. One of the major modern-day concerns of utilities is dealing with such extreme supply outages where operators have used rolling blackouts as a contingency plan to balance supply and demand while serving critical loads. Such events have significant social and economic costs as rolling blackouts are a blunt instrument, depriving customers with low-capacity high-priority loads that provide high amenity (i.e., food refrigeration, telecommunication, etc.). Our contribution presented in this work is a transactive emergency power allocation mechanism that would provide some minimum level of service to all customers while enabling preference-based trading of their allocation. This is in contrast to the state-of-art TE mechanisms that allocate resources to customers solely based on their willingness-to-pay, likely resulting in large inequities. The effectiveness of the proposed mechanism is demonstrated through simulation-based evaluation on a prototypical distribution system experiencing a 12-hour energy scarcity event. Simulation results clearly demonstrate the capability of the proposed transactive emergency allocation mechanism in effectively utilizing almost 100% the available energy and providing some level of service to all customers to operate their high-priority loads throughout the event while being economically efficient.