Several software efforts have been produced over the past few years in various programming languages to help developers handle pseudorandom streams partitioning. Parallel and Distributed Stochastic Simulations (PDSS) can obviously benefit from this kind of high-level tools. The latest release of the Java Development Kit (JDK 7) tries to tackle this problem by providing facilities to partition a pseudorandom stream across various threads thanks to the new class ThreadLocalRandom. Meanwhile, Java 7 offers a framework to split a problem in a divide and conquer way through the new class called ForkJoinPool. As any other Java Thread Pool, ForkJoin exploits threads as workers and manipulates the tasks that will be run on the workers. In Thread- LocalRandom, pseudorandom number generation is handled at a thread level. As a consequence, a scientific application taking advantage of a Java Thread Pool to parallelize its computation may suffer from a bad pseudorandom stream partitioning due to the behaviour of ThreadLocalRandom. The present work introduces TaskLocalRandom, a task-level alternative to ThreadLocalRandom that solves this partitioning problem and assigns an independent pseudorandom stream to each task run in the thread pool. TaskLocalRandom is compatible with existing Java thread pools such as Executors or ForkJoin.