We study the relaxation of an elastic string in a two dimensional pinning landscape using Langevin dynamics simulations. The relaxation of a line, initially flat, is characterized by a growing length, L(t), separating the equilibrated short length scales from the flat long distance geometry that keep memory of the initial condition. We find that, in the long time limit, L(t) has a non-algebraic growth, consistent with thermally activated jumps over barriers with power law scaling, U(L)~Lθ.