A dramatic increase in the total thermal conductivity ( ) is observed in the hidden order (HO) state of single crystal URu 2 Si 2 . Through measurements of the thermal Hall conductivity, we explicitly show that the electronic contribution to is extremely small, so that this large increase in is dominated by phonon conduction. An itinerant BCS or mean-field model describes this behavior well: the increase in is associated with the opening of a large energy gap at the Fermi surface, thereby decreasing electronphonon scattering. Our analysis implies that the ''hidden order'' parameter is strongly coupled to the lattice, suggestive of a broken symmetry involving charge degrees of freedom. DOI: 10.1103/PhysRevLett.97.156401 PACS numbers: 71.27.+a, 71.28.+d, 72.15.Eb At symmetry breaking (2nd order) phase transitions, an ''order parameter'' must characterize the nonsymmetric, low temperature state [1]. The heavy-fermion compound URu 2 Si 2 undergoes a 2nd order phase transition at 17:5 K, yet the order parameter has remained hidden for over 20 years. This is an example of one of the most fundamental problems in solid state physics: the symmetries and associated order parameters are not obvious in many interesting systems. In fact, the order parameters of antiferromagnets (AF, staggered magnetization) and superconductors (SC, condensate wave function phase) were similarly hidden for many years. New discoveries of such nontrivial hidden-order systems (e.g., 2D XY magnets exhibit order of a purely topological character) thus continually expand our understanding of symmetry in solids.Most conceivable experimental probes have been utilized in an attempt to uncover the HO phase. Yet still, this diverse body of experimental data does not seem to convincingly converge to any existing model [2 -4]. For example, some characteristics of AF ordering occur: a large peak appears in the specific heat. However, the tiny observed staggered moment is inconsistent with the entropy lost at the transition [4], instead more likely due to a small AF impurity-phase [5]. Moreover, due to strong hybridization between the conduction electrons and nearly localized U-5f 2 moments, neither a purely local nor itinerantelectron model can be applied. Indeed, there is strong evidence for a Fermi-liquid comprised of ÿ 5 nonKramers doublet degrees of freedom [6,7].We present another route towards uncovering the HO in URu 2 Si 2 via thermal conductivity ( ) measurements. T undergoes a very large increase at the HO transition. Although this feature has been observed before [8,9], a model for T has not been obtained in a way that elucidates the HO. First, we explicitly show that T is dominated by phonons. We then apply a mean-field or BCS framework to describe ph whereby electron-phonon (e-ph) scattering decreases as a gap ( ) in the electronic density of states (DOS) opens at the HO transition. An unusually large 2 0 =k B T C ratio of 8 is needed in order to best describe the data, in agreement with point contact spectroscopy (PCS) estimates of , that...