Frequent closed itemset mining is among the most complex exploratory techniques in data mining, and provides the ability to discover hidden correlations in transactional datasets. The explosion of Big Data is leading to new parallel and distributed approaches. Unfortunately, most of them are designed to cope with low-dimensional datasets, whereas no distributed high-dimensional frequent closed itemset mining algorithms exists. This work introduces PaMPa-HD, a parallel MapReduce-based frequent closed itemset mining algorithm for high-dimensional datasets, based on Carpenter. The experimental results, performed on both real and synthetic datasets, show the efficiency and scalability of PaMPa-HD.