The DNA double-strand breaks that initiate homologous recombination during meiosis are subject to extensive 5′→3′ exonucleolytic processing. This resection is a central and conserved feature of recombination, yet its mechanism is poorly understood. Using a purpose-made deep-sequencing method, we mapped meiotic resection endpoints genome-wide at high spatial resolution in Saccharomyces cerevisiae. Generating full-length resection tracts requires Exo1 exonuclease activity and the DNA-damage responsive kinase Tel1, but not the helicase Sgs1. Tel1 is also required for efficient and timely initiation of resection. We find that distributions of resection endpoints at individual genomic loci display pronounced heterogeneity that reflects a tendency for nucleosomes to block Exo1 in vivo, yet modeling experiments indicate that Exo1 digests chromatin with high apparent processivity and at rates approaching those for naked DNA in vitro. This paradox points to nucleosome destabilization or eviction as a determining feature of the meiotic resection landscape.