An exceptional N=8 superconformal algebra in two dimensions is constructed. It includes a multiplet of Kac-Moody currents in the adjoint representation of Spin(7) and a multiplet of supercurrents in the spinor representation of Spin(7), besides the energy-momentum tensor. It involves both central terms and quadratically non-linear terms in the supercommutators. The Moebius subsuperalgebra is reduced to F(4). The existence of the entire construction is accounted for by the remarkable properties of octonions. (author). 16 refs.