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Gaussian process (GP) regression models make for powerful predictors in out of sample exercises, but cubic runtimes for dense matrix decompositions severely limit the size of data - training and testing - on which they can be deployed. That means that in computer experiment, spatial/geo-physical, and machine learning contexts, GPs no longer enjoy privileged status as data sets continue to balloon in size. We discuss an implementation of local approximate Gaussian process models, in the laGP package for R, that offers a particular sparse-matrix remedy uniquely positioned to leverage modern parallel computing architectures. The laGP approach can be seen as an update on the spatial statistical method of local kriging neighborhoods. We briefly review the method, and provide extensive illustrations of the features in the package through worked-code examples. The appendix covers custom building options for symmetric multi-processor and graphical processing units, and built-in wrapper routines that automate distribution over a simple network of workstations.