This work is concerned with a nonlinear viscoelastic equation with past history. This class of equations was studied by many authors but well-posedness and long-time dynamics were only established recently. The existence of global attractors was considered with additional viscous or frictional damping. In the present work we show that existence of global attractors can be established with the sole weak dissipation given by the memory term. This is done by defining a new multiplier.