We propose an asynchronous, decentralized algorithm for consensus optimization. The algorithm runs over a network of agents, where the agents perform local computation and communicate with neighbors. We design the algorithm so that the agents can compute and communicate independently at different times and for different durations. This reduces the waiting time for the slowest agent or longest communication delay and also eliminates the need for a global clock. Mathematically, the algorithm involves both primal and dual variables, uses fixed step-size parameters, and provably converges to the exact solution under a bounded delay assumption and a random agent assumption. When running synchronously, the algorithm performs just as well as existing competitive synchronous algorithms such as PG-EXTRA, which diverges without synchronization. Numerical experiments confirm the theoretical findings and illustrate the performance of the proposed algorithm.