In the present paper, the existence of a weak time-periodic solution to the nonlinear telegraph equation $U_{tt}+d{U}_t-\sigma {(x,t,U_x)}_x+aU=f(x,t,U_x,U_t,U)$ with the Dirichlet boundary conditions is proved. No “smallness” assumptions are made concerning the function $f$. The main idea of the proof relies on the compensated compactness theory.