This work is concerned with the design of an observer for Switched Linear Systems (SLS) subject to an unknown switching signal. The convergence of the proposed SLS observer is proved, based on observability results for SLS, for the following two cases. First, it is shown that if the discrete state of the SLS is observable, then the observer estimates the switching signal, even though the individual Linear System (LS) may not be observable. And second, it is shown how the observer may provide an estimate of the continuous variables, even though the discrete state is unknown.