When matter is cooled from high temperatures, collective instabilities
develop amongst its constituent particles that lead to new kinds of order. An
anomaly in the specific heat is a classic signature of this phenomenon. Usually
the associated order is easily identified, but sometimes its nature remains
elusive. The heavy fermion metal URu2βSi2β is one such example, where the
order responsible for the sharp specific heat anomaly at T0β=17K has
remained unidentified despite more than seventeen years of effort. In
URu2βSi2β, the coexistence of large electron-electron repulsion and
antiferromagnetic fluctuations in URu2βSi2β leads to an almost incompressible
heavy electron fluid, where anisotropically paired quasiparticle states are
energetically favored. In this paper we use these insights to develop a
detailed proposal for the hidden order in URu2βSi2β. We show that
incommensurate orbital antiferromagnetism, associated with circulating currents
between the uranium ions, can account for the local fields and entropy loss
observed at the 17K transition; furthermore we make detailed predictions for
neutron scattering measurements