This article presents a solution to event-triggered stabilization of a class of nonlinear time-delay systems in the strict-feedback form. Set-valued maps are employed to handle the event-triggered sampling errors, and the closed-loop system is transformed into an interconnection of input-to-state stable subsystems through a set-valued constructive design. The event trigger is designed to satisfy a cyclic-small-gain condition, and the stability of the closed-loop event-triggered system is guaranteed by the cyclic-small-gain theorem for time-delay systems. The proposed design is verified by a practical example of cascade connected reactors.