Transitions to captivity are usually population bottlenecks and so may contribute to the fitness decline of captive-bred species by genetic drift and increased inbreeding. Purging can remove deleterious alleles from populations during declines and bottlenecks but the strength of this effect across different scenarios is unknown. The Lord Howe Island stick insect,Dryococelus australis, has been bred in captivity since 2003 and passed through an extreme bottleneck: only two mating pairs with only one new addition since then. We document extremely low heterozygosity and high inbreeding in the wild, suggestive of low population size and/or a recent colonisation bottleneck. We then test the ability of natural selection to purge deleterious alleles following an extreme population bottleneck by comparing patterns of genetic diversity in wild and captive-bredD. australis. Captive-bred individuals had lower heterozygosity and a greater number of long runs-of-homozygosity compared to wild individuals, implying strong inbreeding in captivity which would facilitate purging. Highly deleterious alleles were preferentially depleted in captivity but all other alleles, coding and non-coding, had the same mean frequency change in captivity compared to the wild. The more deleterious an allele was predicted to be, the more likely it was found outside of runs-of-homozygosity. These results are consistent with inbreeding purging these deleterious alleles. We show that purging can operate on highly deleterious alleles via inbreeding, even after an extreme bottleneck. This may contribute to the persistence of captive populations, although strong drift will also limit their adaptive potential in the future, in captivity and once reintroduced into the wild.