Privacy problems that stem from a lack of truly anonymous communication in today's Internet are exacerbated by growing evidence of large-scale network packet interception and eavesdropping. Internet users have a limited set of tools available at their disposal to enable better communication, including Tor and new protocols such as tcpcrypt and DNS-over-TLS. Content-Centric Networking (CCN) is an emerging (inter-)networking architecture with the goal of becoming an alternative to the IP-based Internet. Such an architecture must at least have parity with IP based solutions for anonymous communication. Thus, there is a clear demand for a CCN analog to Tor and related protocols. ANDANA (Anonymous Named Data Networking Application) was the initial attempt to satisfy this demand for CCNs in the context of the legacy Named Data Networking (NDN) architecture -- an instance of CCN. However, its elementary design and hasty implementation led to performance and usability issues that hinder practical use. In this paper, we introduce AC3N - Anonymous Communication for Content-Centric Networking, a substantially evolved and improved incarnation of ANDANA. AC3N supports high-throughput and low-latency anonymous content retrieval in modern CCNs, for both unidirectional and bidirectional settings. We discuss the design, implementation, performance, and anonymity properties of AC3N. Our experimental results indicate that AC3N incurs very low overhead while providing anonymity features analogous to Tor.