Bacterial microbiomes of incredible complexity are found throughout the world, from exotic marine locations to the soil in our yards to within our very guts. With recent advances in Next-Generation Sequencing (NGS) technologies, we have vastly greater quantities of microbial genome data, but the nature of environmental samples is such that DNA from different species are mixed together. Here, we present Opal for metagenomic binning, the task of identifying the origin species of DNA sequencing reads. Our Opal method introduces low-density, even-coverage hashing to bioinformatics applications, enabling quick and accurate metagenomic binning. Our tool is up to two orders of magnitude faster than leading alignment-based methods at similar or improved accuracy, allowing computational tractability on large metagenomic datasets. Moreover, on public benchmarks, Opal is substantially more accurate than both alignment-based and alignment-free methods (e.g. on SimHC20.500, Opal achieves 95% F1-score while Kraken and CLARK achieve just 91% and 88%, respectively); this improvement is likely due to the fact that the latter methods cannot handle computationally-costly long-range dependencies, which our even-coverage, low-density fingerprints resolve. Notably, capturing these long-range dependencies drastically improves Opal's ability to detect unknown species that share a genus or phylum with known bacteria. Additionally, the family of hash functions Opal uses can be generalized to other sequence analysis tasks that rely on k-mer based methods to encode long-range dependencies.