We estimate a spatially explicit model of the forest clearance process among smallholder farmers in an agricultural frontier of southern Mexico. Our analysis takes as its point of departure a simple utility-maximising model that suggests many possible determinants of deforestation in an economic environment characterised by missing or thin markets. Hypotheses from the model are tested on a data set that combines a time series of satellite imagery with data collected from a survey of farm households whose agricultural plots were geo-referenced using a global positioning system (GPS). We implement a survival analysis to identify the effect of household level explanatory variables on the probability of deforestation. This approach allows us to introduce a measure of the time until clearance as a covariate, thereby affording a control for the effect of potentially important explanatory variables that vary through time but are not directly observable. In addition to identifying several variables relevant for policy analysis, including household demographics, proximity to roads, and government provision of agricultural support, model results suggest that the deforestation process is characterised by non-linear duration dependence, with the probability of forest clearance first decreasing and then increasing with the passage of time.