Tau neutrinos are expected to comprise one third of both the astrophysical and cosmogenic neutrino flux, but currently the flavor ratio is poorly constrained and the expected flux at energies >100 PeV is low. We present a new concept for a radio detector called BEACON sensitive to tau neutrinos with energies greater than 100 PeV in which a radio interferometer searches for upgoing tau neutrinos from a high elevation mountain. Signals from several antennas are coherently summed at the trigger level, permitting not only directional masking of anthropogenic backgrounds, but also a lower trigger threshold. Simulation studies indicate that a modest array size and small number of stations can achieve competitive sensitivity, provided the receivers are at high enough elevation. As a proof of concept, an array of four 30-80 MHz dual polarized antennas was deployed at the White Mountain Research Station.