Content-centric networking -- also known as information-centric networking (ICN) -- shifts emphasis from hosts and interfaces (as in today's Internet) to data. Named data becomes addressable and routable, while locations that currently store that data become irrelevant to applications. Named Data Networking (NDN) is a large collaborative research effort that exemplifies the content-centric approach to networking. NDN has some innate privacy-friendly features, such as lack of source and destination addresses on packets. However, as discussed in this paper, NDN architecture prompts some privacy concerns mainly stemming from the semantic richness of names. We examine privacy-relevant characteristics of NDN and present an initial attempt to achieve communication privacy. Specifically, we design an NDN add-on tool, called ANDaNA, that borrows a number of features from Tor. As we demonstrate via experiments, it provides comparable anonymity with lower relative overhead.