The human Y chromosome exhibits surprisingly low levels of genetic diversity. This could result from neutral processes if the effective population size of males is reduced relative to females due to a higher variance in the number of offspring from males than from females. Alternatively, selection acting on new mutations, and affecting linked neutral sites, could reduce variability on the Y chromosome. Here, using genome-wide analyses of X, Y, autosomal and mitochondrial DNA, in combination with extensive population genetic simulations, we show that low observed Y chromosome variability is not consistent with a purely neutral model. Instead, we show that models of purifying selection are consistent with observed Y diversity. Further, the number of sites estimated to be under purifying selection greatly exceeds the number of Y-linked coding sites, suggesting the importance of the highly repetitive ampliconic regions. While we show that purifying selection removing deleterious mutations can explain the low diversity on the Y chromosome, we cannot exclude the possibility that positive selection acting on beneficial mutations could have also reduced diversity in linked neutral regions, and may have contributed to lowering human Y chromosome diversity. Because the functional significance of the ampliconic regions is poorly understood, our findings should motivate future research in this area. ; Comment: 43 pages, 11 figures