Location discovery is an essential service in modern wireless consumer devices such as smartphones and mobile PCs. Existing anchor or base station-based positioning systems work well in non-hostile scenarios, but their accuracy suffers in the presence of cheating anchors. Securing location discovery in these positioning systems is an important, and still open, research problem. Earlier research efforts in this direction have mainly focused on either efficient detection and elimination of cheating anchors or on localization in the presence of cheating anchors. Proposals on localization in the presence of cheating anchors fail to perform well in the presence of a large number of cheating anchors, whereas, the issue of elimination of cheating anchors (once detected) has not been clearly addressed in techniques that focus on detection and elimination of cheating anchors. In this paper, we present a novel and deterministic strategy for securing anchor-based location discovery. Our technique employs a novel CDMA-based jamming strategy to eliminate (the effect of) cheating anchors during localization. We validate the performance of our proposal under various adversarial strengths and operating scenarios by means of extensive simulations.