This paper develops a theory of patent portfolios in which firms accumulate an enormous amount of related patents, which makes it impractical to develop new products that avoid inadvertent infringement. We show that patent peace arises if product market competition is weak and patent portfolios are either sufficiently weak or sufficiently strong with comparable size. An increase in one firm's patent portfolio reduces the innovation incentives of its rivals but does not necessarily increase its own. Firms with larger patent portfolios have stronger incentives to acquire additional patents, while consumers may be better off if firms with weaker portfolios acquire them. (JEL D43, K11, L13, O34)