Kriging is a spatial interpolation algorithm which provides the best unbiased linear prediction of an observed phenomena by taking a weighted average of samples within a neighbourhood. It is widely used in areas such as geo-statistics where, for example, it may be used to predict the quality of mineral deposits in a location based on previous sample measurements. Kriging has been identified as a good candidate process to be outsourced to a cloud service provider, though outsourcing presents an issue since measurements and predictions may be highly sensitive. We present a method for the private outsourcing of Kriging interpolation using a tailored modification of the Kriging algorithm in combination with homomorphic encryption, allowing crucial information relating to measurement values to be hidden from the cloud service provider.