We use infrared-visible double resonance overtone excitation to prepare HOCl molecules in single, well-characterized rotational levels of high OH stretching states just above the dissociation threshold on the ground potential energy surface. Combined with time-resolved laser induced fluorescence (LIF) detection of the OH product, this approach allows us to monitor the dependence of unimolecular dissociation rate on the angular momentum (J,K-a,K-c), total energy, and vibrational character of the state of the reactant molecule as well as on number of dissociation channels available to the OH product. Dissociation rates from single states of the parent molecule are distributed over more than two orders-of-magnitude in a fashion that appears largely independent of the excess energy and the total angular momentum. In several instances we observe a one-order-of-magnitude difference in dissociation rate between states that are nearby in rotational quantum number and/or energy. Superimposed on these state-to-state rate fluctuations is a general trend toward decreasing unimolecular dissociation rate with increasing K-a quantum number. Moreover, the measured rates, which range from 1 to 300 mu s(-1), are much slower than the predictions of statistical theories. We present a simple model calculation to explain the observed phenomena.