In this brief paper, a Stochastic Model Predictive Control formulation tractable for large-scale systems is developed. The proposed formulation combines the use of Affine Disturbance Feedback, a formulation successfully applied in robust control, with a deterministic reformulation of chance constraints. A novel approximation of the resulting stochastic finite horizon optimal control problem targeted at building climate control is introduced to ensure computational tractability. This work provides a systematic approach toward finding a control formulation which is shown to be useful for the application domain of building climate control. The analysis follows two steps: 1) a small-scale example reflecting the basic behavior of a building, but being simple enough for providing insight into the behavior of the considered approaches, is used to choose a suitable formulation; and 2) the chosen formulation is then further analyzed on a large-scale example from the project OptiControl, where people from industry and other research institutions worked together to create building models for realistic controller comparison. The proposed Stochastic Model Predictive Control formulation is compared with a theoretical benchmark and shown to outperform current control practice for buildings.