A self-avoiding polymer embedded in a two-dimensional quenched random medium consisting of randomly distributed attractive sites has been studied using Monte Carlo methods. It is shown that at a critical temperature the adsorption energy exhibits a sharp transition to a localized state. The transition is characterized by a discontinuity of the adsorption energy at the critical point. The radius of gyration of the chain remains essentially unaffected by the disorder with respect to the chain length dependency. However, there is some evidence that at the critical point the size of the polymer starts to increase with decreasing temperature, Formulas for energy and critical temperature are suggested.