We study the hydrodynamic limit of a anharmonic chain subject to boundary condition in the hyperbolic space-time scale. By suitably adding noise to the Hamiltonian dynamics the macroscopic equation is a nonlinear and isothermal 2x2 system of PDEs (p-system), which can be parabolic or hyperbolic depending on the strength of the noise. In the hyperbolic case we show that the empirical distribution of the microscopic system concentrates on $L^2$-valued solutions of the macroscopic equation, which are "physical" in the sense that they satisfy the second Law of Thermodynamics.