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The aim of this study was to examine the genetic control of time-to-flowering (precocity) in 39 open-pollinated families of Eucalyptus cladocalyx in southern Atacama Desert, Chile, with the view to the selection of trees that flower earlier but with minimal impact on survival and growth. A Bayesian approach, implemented using Gibbs sampling algorithm, was used in data analyses. Precocity was assessed as a binary response at age three and was found to be highly heritable. The estimates of posterior mean and of the 95% posterior interval of the heritability were 0.51 and [0.46-0.56], respectively. Estimated genetic gain ranged from 36.15 to 41.22% (selection intensities of 14.29 and 7.48%, respectively). Total height, basal diameter and survival (measured at age 5) had a positive and relatively moderate genetic correlation with early flowering (r = 0.23, 0.29 and 0.11, respectively) indicating that selection for early flowering alone would have a moderate impact on growth and survival. Early flowering of Eucalyptus cladocalyx was found to be highly heritable in southern Atacama Desert populations, which could be used to improve the honey production in situations where flowers from native species are not available in sufficient quantities.