Does skill-biased technological change benefit less-skilled workers? This paper shows that who gains or loses from SBTC depends on where it occurs across firms and how widely it diffuses across markets. Using Swedish administrative microdata, we document that large firms became increasingly important in the market for skilled labor between 1997 and 2018. Relative to smaller firms, they grew more skill intensive and paid rising skill premia; this steepening reflected a rising large-firm wage premium for college workers but not for non-college workers. We interpret these facts through a model of heterogeneous firms with wage- and price-setting power. The quantified model infers that SBTC became increasingly concentrated among large firms. This concentration raises productivity, but widens wage inequality within and between firms. It can also lower low-skill wages and employment at the firms where SBTC occurs, with negative spillovers to low-skilled workers at competitors. The mechanism is that large firms have weaker scale responses to skill-biased shocks, limiting the expansion that would otherwise offset substitution away from low-skilled labor. Removing firm market power mitigates these losses, but does not overturn them. By contrast, broader diffusion of SBTC across industries can turn those losses into gains for low-skilled workers.