  We construct a chiral theory of gravity in 7 and 8 dimensions, which are
equivalent to Einstein-Cartan theory using less variables. In these dimensions,
we can construct such higher dimensional chiral gravity because of the
existence of gravitational instanton. The octonionic-valued variables in the
theory represent the deviation from the gravitational instanton, and from their
non-associativity, prevents the theory to be SO(n) gauge invariant. Still the
chiral gravity holds G_2 (7-D), and Spin(7) (8-D) gauge symmetry.
