It is well-known that the HVAC (heating, ventilation and air conditioning) dominates electricity consumption in commercial buildings. In this paper, we focus on one of the core problems in building operation, namely chiller sequencing to reduce HVAC electricity consumption. Our contributions are threefold. First, we make a case for why it is important to quantify the performance profile of a chiller, namely coefficient of performance (COP), at run-time, by developing a data-driven COP estimation methodology. Second, we show that predicting COP accurately is a non-trivial problem, requiring considerable computation time. To overcome this barrier, we develop a data-driven COP prediction model and an edge-based chiller sequencing framework integrating the COP predictions, and show that they strike a good balance between electricity saving and ease of use for real-world deployment. Finally, we evaluate the performance of our scheme by applying it to real-world data, spanning 4 years, obtained from multiple chillers across 3 large commercial buildings in Hong Kong. The results show an electricity saving of over 30% compared to baselines. We offer our edge based data-driven chiller sequencing framework as a cost-effective and practical mechanism to reduce electricity consumption associated with HVAC operation in commercial buildings.