We address the challenge of learning safe and robust decision policies in presence of uncertainty in context of the real scientific problem of adaptive resource oversubscription to enhance resource efficiency while ensuring safety against resource congestion risk. Traditional supervised prediction or forecasting models are ineffective in learning adaptive policies whereas standard online optimization or reinforcement learning is difficult to deploy on real systems. Offline methods such as imitation learning (IL) are ideal since we can directly leverage historical resource usage telemetry. But, the underlying aleatoric uncertainty in such telemetry is a critical bottleneck. We solve this with our proposed novel chance-constrained imitation learning framework, which ensures implicit safety against uncertainty in a principled manner via a combination of stochastic (chance) constraints on resource congestion risk and ensemble value functions. This leads to substantial ($\approx 3-4\times$) improvement in resource efficiency and safety in many oversubscription scenarios, including resource management in cloud services.