We consider the strategic interaction between two firms competing for the opportunity to invest in a project with uncertain future values. Starting in complete markets, we provide a rigorous characterization of the strategies followed by each firm in continuous time in the context of a timing/coordination game. In particular, the roles of leader and follower emerge from the resulting symmetric, Markov, sub-game perfect equilibrium. Comparing the expected value obtained by each firm in this case with that obtained when the roles of leader and follower are predetermined, we are able to calculate the amount of money that a firm would be willing to spend in advance (either by paying a license or acquiring market power) to have the right to be the leader in a subsequent game — what we call the priority option. We extend these results to incomplete markets by using utility-indifference arguments.