This paper develops a model of private bilateral contracting, in which an exogenous network determines the pairs of players who can communicate and contract with each other. After contracting, the players interact in an underlying game with globally verifiable productive actions and externally enforced transfers. The paper investigates whether such decentralized contracting can internalize externalities that arise due to parties being unable to contract directly with others whose productive actions affect their payoffs. The contract‐formation protocol, called the “contracting institution,” is treated as a design element. The main result is positive: There is a contracting institution that supports efficient equilibria for any underlying game and connected network. A critical property is that the institution allows for sequential contract formation or revision. The equilibrium construction features assurance contracts and cancellation penalties.