  Ultra-cold gases excited to strongly interacting Rydberg states are a
promising system for quantum simulations of many-body systems. For off-resonant
excitation of such systems in the dissipative regime, highly correlated
many-body states exhibiting, among other characteristics, intermittency and
multi-modal counting distributions are expected to be created. So far,
experiments with Rydberg atoms have been carried out in the resonant,
non-dissipative regime. Here we realize a dissipative gas of rubidium Rydberg
atoms and measure its full counting statistics for both resonant and
off-resonant excitation. We find strongly bimodal counting distributions in the
off-resonant regime that are compatible with intermittency due to the
coexistence of dynamical phases. Moreover, we measure the phase diagram of the
system and find good agreement with recent theoretical predictions. Our results
pave the way towards detailed studies of many-body effects in Rydberg gases.
