Antarctic krill (Euphausia superba; hereafter krill) are an incredibly abundant pelagic crustacean which has a wide, but patchy, distribution in the Southern Ocean. Several studies have examined the potential for population genetic structuring in krill, but DNA-based analyses have focused on a limited number of markers and have covered only part of their circum-Antarctic range. We used mitochondrial DNA and restriction site-associated DNA sequencing (RAD-seq) to investigate genetic differences between krill from five sites, including two from East Antarctica. Our mtDNA results show no discernible genetic structuring between sites separated by thousands of kilometres, which is consistent with previous studies. Using standard RAD-seq methodology, we obtained over a billion sequences from >140 krill, and thousands of variable nucleotides were identified at hundreds of loci. However, downstream analysis found that markers with sufficient coverage were primarily from multicopy genomic regions. Careful examination of these data highlights the complexity of the RAD-seq approach in organisms with very large genomes. To characterize the multicopy markers, we recorded sequence counts from variable nucleotide sites rather than the derived genotypes; we also examined a small number of manually curated genotypes. Although these analyses effectively fingerprinted individuals, and uncovered a minor laboratory batch effect, no population structuring was observed. Overall, our results are consistent with panmixia of krill throughout their distribution. This result may indicate ongoing gene flow. However, krill's enormous population size creates substantial panmictic inertia, so genetic differentiation may not occur on an ecologically relevant timescale even if demographically separate populations exist.