The phase diagram of three-dimensional (3d) simplicial quantum gravity is studied using the Monte-Carlo simulation method. It is found that the behavior of the entropy of manifolds, unambiguously defined in this discrete formulation, insures the existence of a vacuum, in spite of the Einstein action being bottomless. A critical line is found as well as some evidence for the existence of a tricritical point. Only to the right of this point, where the bare coupling of the Einstein term in the action is strong enough, a sensible continuum limit can possibly exist.