The mammalian Y Chromosome sequence, critical for studying male fertility and dispersal, is enriched in repeats and palindromes, and thus, is the most difficult component of the genome to assemble. Previously, expensive and labor-intensive BAC-based techniques were used to sequence the Y for a handful of mammalian species. Here, we present a much faster and more affordable strategy for sequencing and assembling mammalian Y Chromosomes of sufficient quality for most comparative genomics analyses and for conservation genetics applications. The strategy combines flow sorting, short- and long-read genome and transcriptome sequencing, and droplet digital PCR with novel and existing computational methods. It can be used to reconstruct sex chromosomes in a heterogametic sex of any species. We applied our strategy to produce a draft of the gorilla Y sequence. The resulting assembly allowed us to refine gene content, evaluate copy number of ampliconic gene families, locate species-specific palindromes, examine the repetitive element content, and produce sequence alignments with human and chimpanzee Y Chromosomes. Our results inform the evolution of the hominine (human, chimpanzee, and gorilla) Y Chromosomes. Surprisingly, we found the gorilla Y Chromosome to be similar to the human Y Chromosome, but not to the chimpanzee Y Chromosome. Moreover, we have utilized the assembled gorilla Y Chromosome sequence to design genetic markers for studying the male-specific dispersal of this endangered species.