Since WSNs have restricted energy sources, the energy efficiency of a synchronization scheme is as important as the accuracy of a clock. To accomplish both the energy efficiency and the accuracy, we propose a new clock synchronization scheme called Chaining Clock Synchronization (CCS). In CCS, a subset of nodes whose transmission range cover the overall network carries out a two-way message exchange algorithm while the remaining nodes synchronize themselves by overhearing the messages. To reduce the energy consumption associated with the message exchange, CCS integrates a clock request and a clock reply into a single message. Therefore, CCS requires only a single message transmission per node for the synchronization. To increase the accuracy of the clock synchronization, we also propose a new technique called clock skew propagation to reduce the error accumulation associated with multi-hop clock synchronization schemes. According to the results from NS-2, in comparison with TPSN, CCS can effectively reduce the energy consumption by up to 95% while sacrificing 9.2% of the average accuracy of clocks. Moreover, the average clock error accumulation of CCS is reduced by 58% as the hop distance from a reference node increases.