Grammars for machine translation can be materialized on demand by finding source phrases in an indexed parallel corpus and extracting their translations. This approach is limited in practical applications by the computational expense of online lookup and extraction. For phrase-based models, recent work has shown that on-demand grammar extraction can be greatly accelerated by parallelization on general purpose graphics processing units (GPUs), but these algorithms do not work for hierarchical models, which require matching patterns that contain gaps. We address this limitation by presenting a novel GPU algorithm for on-demand hierarchical grammar extraction that is at least an order of magnitude faster than a comparable CPU algorithm when processing large batches of sentences. In terms of end-to-end translation, with decoding on the CPU, we increase throughput by roughly two thirds on a standard MT evaluation dataset. The GPU necessary to achieve these improvements increases the cost of a server by about a third. We believe that GPU-based extraction of hierarchical grammars is an attractive proposition, particularly for MT applications that demand high throughput.