Frequent-itemset mining is an essential part of the association rule mining process, which has many application areas. It is a computation and memory intensive task with many opportunities for optimization. Many efficient sequential and parallel algorithms were proposed in the recent years. Most of the parallel algorithms, however, cannot cope with the huge number of threads that are provided by large multiprocessor or many-core systems. In this paper, we provide a highly parallel version of the well-known Eclat algorithm. It runs on both, multiprocessor systems and many-core coprocessors, and scales well up to a very large number of threads---244 in our experiments. To evaluate mcEclat's performance, we conducted many experiments on realistic datasets. mcEclat achieves high speedups of up to 11.5x and 100x on a 12-core multiprocessor system and a 61-core Xeon Phi many-core coprocessor, respectively. Furthermore, mcEclat is competitive with highly optimized existing frequent-itemset mining implementations taken from the FIMI repository.