To achieve true scalability on massive datasets, a modern query engine needs to be able to take advantage of large, shared-memory, multicore systems. Binary joins are conceptually easy to parallelize on a multicore system; however, several applications require a different approach to query evaluation, using a Worst-Case Optimal Join (WCOJ) algorithm. WCOJ is known to outperform traditional query plans for cyclic queries. However, there is no obvious adaptation of WCOJ to parallel architectures. The few existing systems that parallelize WCOJ do this by partitioning only the top variable of the WCOJ algorithm. This leads to work skew (since some relations end up being read entirely by every thread), possible contention between threads (when the hierarchical trie index is built lazily, which is the case on most recent WCOJ systems), and exacerbates the redundant computations already existing in WCOJ. We introduce HoneyComb, a parallel version of WCOJ, optimized for large multicore, shared-memory systems. HoneyComb partitions the domains of all query variables, not just that of the top loop. We adapt the partitioning idea from the HyperCube algorithm, developed by the theory community for computing multi-join queries on a massively parallel shared-nothing architecture, and introduce new methods for computing the shares, optimized for a shared-memory architecture. To avoid the contention created by the lazy construction of the trie-index, we introduce CoCo, a new and very simple index structure, which we build eagerly, by sorting the entire relation. Finally, in order to remove some of the redundant computations of WCOJ, we introduce a rewriting technique of the WCOJ plan that factors out some of these redundant computations. Our experimental evaluation compares HoneyComb with several recent implementations of WCOJ.