ProbitSpatial R package: fast and accurate spatial probit estimations. This package meets the emerging needs of powerful and reliable models for the analysis of spatial discrete choice data. Since the explosion of available and voluminous geospatial and location data, older estimation techniques cannot withstand the course of dimensionality and are restricted to samples with less than a few thousand observations. The functions contained in ProbitSpatial allow fast and accurate estimations of Spatial Autoregressive and Spatial Error Models under Probit specification. They are based on the full maximization of likelihood of an approximate multivariate normal distribution function, a task that was considered as prodigious just few years ago. Extensive simulation and empirical studies proved that these functions can readily handle sample sizes with as many as several millions of observations, provided the spatial weight matrix is in convenient sparse form, as is typically the case of large data sets, where each observation neighbours only a few other observations. SpatialProbit relies amongst others on Rcpp, RcppEigen and Matrix packages to produce fast computations for large sparse matrixes. Possible applications of spatial binary choice models include spread of diseases and pathogens, plants distribution, technology and innovation adoption, deforestation, land use change, amongst many others.