Recently many important biopolymers have been found to possess intrinsic curvature. Tubulin protofilaments in animal cells, FtsZ filaments in bacteria and double stranded DNA are examples. We examine how intrinsic curvature influences the conformational statistics of such polymers. We give exact results for the tangent-tangent spatial correlation function C (r) = t (s). t (s+r), both in two and three dimensions. Contrary to expectation, C (r) does not show any oscillatory behavior, rather decays exponentially and the effective persistence length has strong length dependence for short polymers. We also compute the distribution function P (R) of the end to end distance R and show how curved chains can be distinguished from wormlike chains using loop formation probability.