Several research works have focused on supporting index access in MapReduce systems. These works have allowed users to significantly speed up selective MapReduce jobs by orders of magnitude. However, all these proposals require users to create indexes upfront, which might be a difficult task in certain applications (such as in scientific and social applications) where workloads are evolving or hard to predict. To overcome this problem, we propose LIAH (Lazy Indexing and Adaptivity in Hadoop), a parallel, adaptive approach for indexing at minimal costs for MapReduce systems. The main idea of LIAH is to automatically and incrementally adapt to users' workloads by creating clustered indexes on HDFS data blocks as a byproduct of executing MapReduce jobs. Besides distributing indexing efforts over multiple computing nodes, LIAH also parallelises indexing with both map tasks computation and disk I/O. All this without any additional data copy in main memory and with minimal synchronisation. The beauty of LIAH is that it piggybacks index creation on map tasks, which read relevant data from disk to main memory anyways. Hence, LIAH does not introduce any additional read I/O-costs and exploit free CPU cycles. As a result and in contrast to existing adaptive indexing works, LIAH has a very low (or invisible) indexing overhead, usually for the very first job. Still, LIAH can quickly converge to a complete index, i.e. all HDFS data blocks are indexed. Especially, LIAH can trade early job runtime improvements with fast complete index convergence. We compare LIAH with HAIL, a state-of-the-art indexing technique, as well as with standard Hadoop with respect to indexing overhead and workload performance.