It is well-known that the HVAC (heating, ventilation and air conditioning) dominates electricity consumption in commercial buildings. Alongside, electricity prices are increasing in several nations around the world, putting pressure on facility managers to reduce the electricity consumption incurred in operating their HVAC and buildings. In this paper, we focus on one of the core problems in building operation, namely chiller sequencing for reducing 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 runtime, 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 dominant-graph based COP prediction technique and a time-constrained chiller sequencing algorithm integrating the COP predictions, which strikes a good balance between electricity consumption reduction 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 that our solution is able to save on average 21 MWh of electricity consumption in each of the 3 buildings, which is an improvement of over 30% compared to the current mode of operation of the chillers in the buildings. We offer our data-driven chiller sequencing framework under time constraints as an effective and practical mechanism for reducing the electricity consumption associated with HVAC operation in commercial buildings.