Spin-glass and chiral-glass orderings of the three-dimensional Heisenberg spin glass are studied by large-scale equilibrium Monte Carlo simulations. A finite-size scaling analysis of the squared order parameters both for spin and chirality shows that a freezing temperature of the spin-glass order is lower than that of the chiral-glass one, namely there exists a chiral glass phase in which the chirality exhibits a long range order without a conventional spin glass order. Our results support a spin-chirality decoupling picture, which is a basic assumption of a chirality scenario of experimentally observed spin-glass transition.