We study the problem of implementing social choice correspondences using the concept of undominated Nash equilibrium, i.e. Nash equilibrium in which no one uses a weakly dominated strategy. We show that this mild refinement of Nash equilibrium has a dramatic impact on the set of implementable correspondences. Our main result is that if there are at least three agents in the society, then any correspondence which satisfies the usual no veto power condition is implementable unless some agents are completely indifferent over all possible outcomes. Many common welfare criteria, such as the Pareto correspondence, and several familiar voting rules, such as majority and plurality rules, satisfy our conditions. This possibility result stands in sharp contrast to the more restrictive findings with implementation in either Nash equilibrium or subgame perfect equilibrium. We present several examples to illustrate the difference between undominated Nash implementation and implementation with alternative solution concepts.