Autonomous electronic circuits provide a convenient framework in which to study chaotic phenomena. These systems are easy to build, easy to measure, and easy to model using differential and difference equations. Furthermore, they operate in real time, and parameter values are readily adjusted. In this work, we discuss the nature of chaotic steady-state behaviour and describe how it manifests itself in autonomous electronic circuits. We study state space, time- and frequency-domain measurement techniques for characterizing steady-state behaviour. Because of its value as a paradigm for exploring chaos, we choose Chua's oscillator as the vehicle for our experiments.