Ecological theory has grappled for fifty years with the “diversity-stability debate”. On the one hand, random matrix arguments due to Robert May imply that large, complex ecosystems cannot be stable. On the other hand, empirical observations suggests that communities are usually stabilized (rather than destabilized) by diversity—the opposite of May’s prediction. In this talk, I will propose a resolution of this puzzle based on recently discovered ecosystem-level scaling laws relating productivity to biomass. Using a simple modification of the Generalized Lotka Volterra model, I will show that May’s conclusion is reversed when the growth of populations is sublinear rather than logistic. The talk is intended for physicists (I am one), and will include data, theory, and simulations.