In　this　study,the　event-triggered　asymptotic　tracking　control　problem　is　considered　for　a　class　of　nonholonomic　systems　in　chained　form　for　the　time-varying　reference　input.First,to　eliminate　the　ripple　phenomenon　caused　by　the　imprecise　compensation　of　the　time-varying　reference　input,a　novel　time-varying　event-triggered　piecewise　continuous　control　law　and　a　triggering　mechanism　with　a　time-varying　triggering　function　are　developed.Second,an　explicit　integral　input-to-state　stable　Lyapunov　function　is　constructed　for　the　time-varying　closed-loop　system　regarding　the　sampling　error　as　the　external　input.The　origin　of　the　closed-loop　system　is　shown　to　be　uniformly　globally　asymptotically　stable　for　any　global　exponential　decaying　threshold　signals,which　in　turn　rules　out　the　Zeno　behavior.Moreover,infinitely　fast　sampling　can　be　avoided　by　appropriately　tuning　the　exponential　convergence　rate　of　the　threshold　signal.A　numerical　simulation　example　is　provided　to　illustrate　the　proposed　control　approach.