This paper explains how to stabilize a "nonholonomic integrator" using a hybrid control law employing switching and logic. Results concerning asymptotic stability and exponential convergence to the origin are derived. The notion of a (positively) invariant set is extended to hybrid systems and sufficient conditions for invariance are presented. The verification of these conditions does not require the computation of the state trajectories and their use goes beyond the analysis of the system presented in this paper.