Generation-based fuzzing is a software testing approach which is able to discover different types of bugs and vulnerabilities in software. It is, however, known to be very time consuming to design and fine tune classical fuzzers to achieve acceptable coverage, even for small-scale software systems. To address this issue, we investigate a machine learning-based approach to fuzz testing in which we outline a family of test-case generators based on Recurrent Neural Networks (RNNs) and train those on readily available datasets with a minimum of human fine tuning. The proposed generators do, in contrast to previous work, not rely on heuristic sampling strategies but principled sampling from the predictive distributions. We provide a detailed analysis to demonstrate the characteristics and efficacy of the proposed generators in a challenging web browser testing scenario. The empirical results show that the RNN-based generators are able to provide better coverage than a mutation based method and are able to discover paths not discovered by a classical fuzzer. Our results supplement findings in other domains suggesting that generation based fuzzing with RNNs is a viable route to better software quality conditioned on the use of a suitable model selection/analysis procedure.