The HEPiX (http: //www.hepix.org) IPv6 Working Group has been investigating the many issues which feed into the decision on the timetable for the use of IPv6 (http://www.ietf.org/rfc/rfc2460.txt) networking protocols in High Energy Physics (HEP) Computing, in particular in the Worldwide Large Hadron Collider (LHC) Computing Grid (WLCG). RIPE NCC, the European Regional Internet Registry (RIR), ran out of IPv4 addresses in September 2012. The North and South America RIRs are expected to run out soon. In recent months it has become more clear that some WLCG sites, including CERN, are running short of IPv4 address space, now without the possibility of applying for more. This has increased the urgency for the switch-on of dual-stack IPv4/IPv6 on all outward facing WLCG services to allow for the eventual support of IPv6-only clients. The activities of the group include the analysis and testing of the readiness for IPv6 and the performance of many required components, including the applications, middleware, management and monitoring tools essential for HEP computing. Many WLCG Tier 1/2 sites are participants in the group's distributed IPv6 testbed and the major LHC experiment collaborations are engaged in the testing. We are constructing a group web/wiki which will contain useful information on the IPv6 readiness of the various software components and a knowledge base (http://hepix-ipv6.web.cern.ch/knowledge-base). This paper describes the work done by the working group and its future plans.