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Deep learning models have achieved expert-level performance in healthcare with an exclusive focus on training accurate models. However, in many clinical environments such as intensive care unit (ICU), real-time model serving is equally if not more important than accuracy, because in ICU patient care is simultaneously more urgent and more expensive. Clinical decisions and their timeliness, therefore, directly affect both the patient outcome and the cost of care. To make timely decisions, we argue the underlying serving system must be latency-aware. To compound the challenge, health analytic applications often require a combination of models instead of a single model, to better specialize individual models for different targets, multi-modal data, different prediction windows, and potentially personalized predictions. To address these challenges, we propose HOLMES-an online model ensemble serving framework for healthcare applications. HOLMES dynamically identifies the best performing set of models to ensemble for highest accuracy, while also satisfying sub-second latency constraints on end-to-end prediction. We demonstrate that HOLMES is able to navigate the accuracy/latency tradeoff efficiently, compose the ensemble, and serve the model ensemble pipeline, scaling to simultaneously streaming data from 100 patients, each producing waveform data at 250~Hz. HOLMES outperforms the conventional offline batch-processed inference for the same clinical task in terms of accuracy and latency (by order of magnitude). HOLMES is tested on risk prediction task on pediatric cardio ICU data with above 95% prediction accuracy and sub-second latency on 64-bed simulation.