Insulators occur in more than one guise, a recent finding was a class of topological insulators, which host a conducting surface juxtaposed with an insulating bulk. Here we report the observation of an unusual insulating state with an electrically insulating bulk that simultaneously yields bulk quantum oscillations with characteristics of an unconventional Fermi liquid. We present quantum oscillation measurements of magnetic torque in high purity single crystals of the Kondo insulator SmB 6 , which reveal quantum oscillation frequencies characteristic of a large three-dimensional conduction electron Fermi surface similar to the metallic rare earth hexaborides such as PrB 6 and LaB 6 . The quantum oscillation amplitude strongly increases at low temperatures, appearing strikingly at variance with conventional metallic behaviour.Kondo insulators, a class of materials positioned close to the border between insulating and metallic behaviour, provide fertile ground for unusual physics [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. This class of strongly correlated materials is thought to be characterised by a 1 arXiv:1507.01129v1 [cond-mat.str-el] 4 Jul 2015