The ‘thrifty gene hypothesis’ suggests genetic susceptibility to obesity arises because of positive selection for alleles favored fat deposition and survival during famines. We used public domain data to locate signatures of positive selection based on derived allele frequency, genetic diversity, long haplotypes and differences between populations at single nucleotide polymorphisms (SNPs) identified in genome wide association studies (GWAS) for Body Mass Index (BMI). We used SNPs near the lactase (LCT), SLC24A5 and SLC45A2 genes as positive controls, and 120 randomly-selected SNPs as negative controls. We found evidence for positive selection (p<0.05) at nine out of 115 BMI SNPs. However, five of these involved positive selection for the protective allele (i.e. for leanness). The widespread absence of signatures of positive selection, combined with selection favoring leanness at some alleles, does not support the idea that obesity provided a selective advantage to survive historical periods of famine, or other selective advantage.