We explore the dynamics of group inequality when segregation of social networks places the initially less affluent group at a disadvantage in acquiring human capital. Extending Loury (1977), we demonstrate that (i) group differences in economic success can persist across generations in the absence of either discrimination or group differences in ability, provided that social segregation is sufficiently great, (ii) there is a threshold level of integration above which group inequality cannot be sustained, (iii) this threshold varies systematically but non-monotonically with the population share of the disadvantaged group, (iv) crossing the threshold induces convergence to a common high level of human capital if the less affluent population share is sufficiently small (and the opposite, otherwise), and (v) a race-neutral policy that reduces the cost of acquiring human capital can expand the range over which reducing segregation can be Pareto-improving.