  One of the few remaining unknowns in the standard three-flavor neutrino
oscillation paradigm is the ordering of neutrino masses. In this work we
propose a novel method for determining neutrino mass ordering using the time
information on early supernova neutrino events. In a core-collapse supernova,
neutrinos are produced earlier than antineutrinos and, depending on the mass
ordering which affects the adiabatic flavor evolution, may cause earlier
observable signals in $\nu_e$ detection channels than in others. Hence, the
time differences are sensitive to the mass ordering. We find that using the
time information on the detection of the first galactic supernova events at
future detectors like DUNE, JUNO and Hyper-Kamiokande, the mass ordering can
already be determined at $\sim 2 \sigma$ CL, while $\mathcal{O}(10)$ events
suffice for the discovery. Our method does not require high statistics and
could be used within the supernova early warning system (SNEWS) which will have
access to the time information on early supernova neutrino events recorded in a
number of detectors. The method proposed in this paper also implies a crucial
interplay between the mass ordering and the triangulation method for locating
supernovae.
