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We present a stochastic model predictive control (MPC) framework for central heating, ventilation, and air conditioning (HVAC) plants. The framework uses real data to forecast and quantify uncertainty of disturbances affecting the system over multiple timescales (electrical loads, heating/cooling loads, and energy prices). We conduct detailed closed-loop simulations and systematic benchmarks for the central HVAC plant of a typical university campus. Results demonstrate that deterministic MPC fails to properly capture disturbances and that this translates into economic penalties associated with peak demand charges and constraint violations in thermal storage capacity (overflow and/or depletion). Our results also demonstrate that stochastic MPC provides a more systematic approach to mitigate uncertainties and that this ultimately leads to cost savings of up to 7.5% and to mitigation of storage constraint violations. Benchmark results also indicate that these savings are close to ideal savings (9.6%) obtained under MPC with perfect information.