A quantum system which can tunnel, at T=0, out of a metastable state and whose interaction with its environment is adequately described in the classically accessible region by a phenomenological friction coefficient, is considered. By only assuming that the environment response is linear, it is found that dissipation multiplies the tunneling probability by the factor ехр[-Ат)(Д^JД], where Aq is the "distance under the barrier" and A is a numerical factor which is generally of order unity.