We quantize the N = 8 supersymmetric singleton field theory which is formulated on the boundary of the four-dimensional anti-de Sitter spacetime (ADS4). The theory has rigid OSp(8, 4) symmetry which acts as a superconformal group on the boundary of AdS4. We show that the generators of this symmetry satisfy the full quantum OSp(8, 4) algebra. The spectrum of the theory contains massless states of all higher integer and half-integer spin which fill the irreducible representations of OSp(8, 4) with highest spin smax = 2,4,6,... . Remarkably, these are in one-to-one correspondence with the generators of Vasiliev's infinite-dimensional extended higher spin superalgebra shs(8, 4), suggesting that we may have stumbled onto a field-theoretic realization of this algebra. We also discuss the possibility of a connection between the N = 8 supersingleton theory with the eleven-dimensional supermembrane in an AdS4 Ã— S7 background.