A decentralized event-triggered control scheme is developed for the containment control problem. An estimate-based decentralized controller is designed for each agent so that it is only required to communicate with neighboring agents at discrete event times. These events are determined by a decentralized trigger function that only requires local information. Different from conventional strategies, the developed control approach does not require continuous communication with local neighboring follower agents for state feedback, reducing communication bandwidth. The event-triggered approach is facilitated by developing a positive constant lower bound on the inter-event interval, which indicates Zeno behavior is avoided. A Lyapunov-based convergence analysis is provided to indicate asymptotic convergence of the developed strategy.