The levels and distribution of standing genetic variation in a genome can provide a wealth of insights about the adaptive potential, demographic history, and genome structure of a population or species. As structural variants are increasingly associated with traits important for adaptation and speciation, investigating both sequence and structural variation is essential for wholly tapping this potential. Using a combination of shotgun sequencing, 10X Genomics linked reads and proximity-ligation data (Chicago and Hi-C), we produced and annotated a chromosome-level genome assembly for the Atlantic silverside (Menidia menidia) - an established ecological model for studying the phenotypic effects of natural and artificial selection - and examined patterns of genomic variation across two individuals sampled from different populations with divergent local adaptations. Levels of diversity varied substantially across each chromosome, consistently being highly elevated near the ends (presumably near telomeric regions) and dipping to near zero around putative centromeres. Overall, our estimate of the genome-wide average heterozygosity in the Atlantic silverside is the highest reported for a fish, or any vertebrate, to date (1.32-1.76% depending on inference method and sample). Furthermore, we also found extreme levels of structural variation, affecting ~23% of the total genome sequence, including multiple large inversions (> 1 Mb and up to 12.6 Mb) associated with previously identified haploblocks showing strong differentiation between locally adapted populations. These extreme levels of standing genetic variation are likely associated with large effective population sizes and may help explain the remarkable adaptive divergence among populations of the Atlantic silverside.