Can the existence of positive productivity spillovers between co-workers be explained by the presence of complementarities in a firm's production function? A simple model demonstrates that this is possible when workers perform their tasks sequentially and part of individuals' pay is determined by the firm's output, but also that negative spillovers may arise when workers can raise overall output unilaterally. Data from major league baseball support these predictions. They show that the pairs of players who are most complementary in the production process exert the largest positive spillovers on each other, but that negative spillovers predominate between all player pairs.