This study evaluates a probabilistic forecast-driven, chance-constrained model predictive control (MPC) framework for whole-building peak mitigation in a hot-desert large office. In a ten-week summer co-simulation of a 20-story office at 5-minute supervisory cadence (50 weekdays), daily site electricity decreased by 5,339 kWh/ day (14.0%) and the daily 15-minute peak demand decreased by 1,771 kW (24.9%) relative to rule-based control. Daily heating, ventilation, and air-conditioning (HVAC) electricity decreased by 19.0%. Occupied-hour operative-temperature compliance averaged 96.7% under MPC versus 92.4% under rule-based control, and the worst day under MPC had 93.8% compliance with a maximum operative-temperature excursion of 1.6 degrees Celsius and a longest consecutive violation of 15 min. Online optimization met the 5-minute cadence, with a median solve time of 1.21 s, a 99th percentile of 4.34 s, and a watchdog fallback rate of 0.21%. The forecasting layer combined gradient-boosted trees (XGBoost), a Temporal Convolutional Network (TCN), and an autoregressive integrated moving average model with exogenous inputs (ARIMAX) to produce 1 to 6 h mean and quantile site-power forecasts, and those quantiles parameterized chance constraints in the MPC. Under 20% forecast perturbations, energy increased by at most 1.1% with peaks essentially unchanged. The evaluation is simulation-based and limited to cooling-dominated summer operation, so field trials remain necessary to confirm performance under real sensing, faults, and multiseasonal weather.