We consider the contact process on the preferential attachment graph. The work of Berger, Borgs, Chayes and Saberi [BBCS1] confirmed physicists predictions that the contact process starting from a typical vertex becomes endemic for an arbitrarily small infection rate $λ$ with positive probability. More precisely, they showed that with probability $λ^{Θ(1)}$, it survives for a time exponential in the largest degree. Here we obtain sharp bounds for the density of infected sites at a time close to exponential in the number of vertices (up to some logarithmic factor).