In this paper we propose a strategy for administering a survey that is mindful of sensitive data and individual privacy. The survey in question seeks to estimate the population proportions of a sensitive, polychotomous variable and does not depend on anonymity, cryptography, or in legal guarantees for its privacy preserving properties. Our technique, called Negative Surveys, presents interviewees with a question and t possible answers, and asks participants to eliminate one of t-1 alternatives at random. The method is closely related to randomized response techniques (RRTs) in that both rely on a random component to preserve privacy; however, while RRTs require respondents to choose among questions and give an answer, negative surveys ask them to choose between possible answers to a single question. This distinction has important consequences for the privacy, methodology, and reliability of our scheme. In the course of the paper we quantify the amount of information surrendered by an interviewee, elaborate on how to estimate the desired population proportions, and discuss the properties of our method at length. We also introduce a specific setup that requires a single coin as a randomizing device, and that limits the amount of information each respondent is exposed to by presenting to them only a subset of the question's alternatives.