The self-triggered event-based control of uncertain nonholonomic systems in the chained form is studied for the first time in this paper. In order to tackle the effects of drift uncertain nonlinearities, nonholonomic constraints and nonsmooth aperiodic sampling in event-based control, a novel systematic design scheme is proposed by integrating set-valued maps with state-separation and state-scaling techniques. The stability analysis of the closed-loop self-triggered control system is based on the cyclic-small-gain theorem that overcomes the limitation of Lyapunov theory in the construction of Lyapunov functions for nonsmooth dynamical systems. More specifically, the closed-loop self-triggered control system is transformed into an interconnection of multiple input-to-state stable systems, to which the cyclic-small-gain theorem is applied for robust stability analysis. Interestingly, the proposed design approach is also applicable to a broader class of nonholonomic systems subject to state and input-dependent uncertainties, and the result is still new even if the plant is reduced to the ideal unperturbed chained form. The main result is validated by a benchmark example of mobile robots subject to parametric uncertainties and a measurement noise such as bias in orientation.