A holographic duality is proposed relating quantum gravity on dS_D (D-dimensional de Sitter space) to conformal field theory on a single S^{D-1} ((D-1)-sphere), in which bulk de Sitter correlators with points on the boundary are related to CFT correlators on the sphere, and points on I^+ (the future boundary of dS_D) are mapped to the antipodal points on S^{D-1} relative to those on I^-. For the case of dS_3, which is analyzed in some detail, the central charge of the CFT_2 is computed in an analysis of the asymptotic symmetry group at I^\pm. This dS/CFT proposal is supported by the computation of correlation functions of a massive scalar field. In general the dual CFT may be non-unitary and (if for example there are sufficently massive stable scalars) contain complex conformal weights. We also consider the physical region O^- of dS_3 corresponding to the causal past of a timelike observer, whose holographic dual lives on a plane rather than a sphere. O^- can be foliated by asymptotically flat spacelike slices. Time evolution along these slices is generated by L_0+\bar L_0, and is dual to scale transformations in the boundary CFT_2.