We show that the charge and thermal transport measurements on ultraclean crystals of URu2Si2 reveal a number of unprecedented superconducting properties. The uniqueness is best highlighted by the peculiar field dependence of thermal conductivity including the first order transition at Hc2 with a reduction of entropy flow. This is a consequence of multi-band superconductivity with compensated electronic structure in the hidden order state of this system. We provide strong evidence for a new type of unconventional superconductivity with two distinct gaps having different nodal topology.The heavy-Fermion compound URu 2 Si 2 has mystified researchers since the superconducting state (T c = 1.5 K) is embedded within the "hidden order" phase (T h = 17.5 K) [1,2,3]. Although several exotic order parameters have been proposed for the hidden order phase [4], it is not identified yet. According to several experimental observations, most of the carriers disappear below T h resulting in a density one order of magnitude smaller than in other heavy-Fermion superconductors [5,6,7]. Superconductivity with such a low density is remarkablesince the superfluid density is very low in some way reminiscent of underdoped cuprates. Moreover, pressure studies reveal that the superconductivity coexists with the hidden order but is suppressed by antiferromagnetic ordering [8].In this Letter, using ultraclean single crystals, we report various anomalous superconducting properties in URu 2 Si 2 . We show that a peculiar electronic structure appearing below the hidden order transition provides an intriguing stage on which a new type of unconventional superconducting state appears.Single crystals of URu 2 Si 2 were grown by the Czochralski pulling method in a tetra-arc furnace. The welldefined superconducting transition was confirmed by the specific heat measurements. The thermal conductivity κ was measured using a standard four-wire steady state method along the a-axis (heat current q a). The contact resistance at low temperatures is less than 10 mΩ.We first discuss the electronic structure below T h . Figure 1 shows the temperature dependence of the resistivity ρ along the a-axis and Hall coefficient R H (solid circles) defined as R H ≡ dρxy dH at H → 0 T for H c in the tetragonal crystal structure. In zero field, ρ depends on T as ρ = ρ 0 + AT 2 below 6 K down to T c . The exceptionally low residual resistivity ρ 0 = 0.48 µΩ cm and large residual resistivity ratio RRR = 670 attest the highest crystal quality currently achievable. R H exhibits an eight-fold increase below T h and attains a T -independent value at low temperatures, associated with a strong reduction of the carrier density. Most remarkably, the magnetoresistance (MR) increases with decreasing temperature and becomes extremely large at the lowest temperatures. The inset of Fig.