Remote identification and mapping of canopy tree species can contribute valuable information towards our understanding of ecosystem biodiversity and function over large spatial scales. However, the extreme challenges posed by highly diverse, closed-canopy tropical forests have prevented automated remote species mapping of non-flowering tree crowns in these ecosystems. We set out to identify individuals of three focal canopy tree species amongst a diverse background of tree and liana species on Barro Colorado Island, Panama, using airborne imaging spectroscopy data. First, we compared two leading single-class classification methods—binary support vector machine (SVM) and biased SVM—for their performance in identifying pixels of a single focal species. From this comparison we determined that biased SVM was more precise and created a multi-species classification model by combining the three biased SVM models. This model was applied to the imagery to identify pixels belonging to the three focal species and the prediction results were then processed to create a map of focal species crown objects. Crown-level cross-validation of the training data indicated that the multi-species classification model had pixel-level producer’s accuracies of 94–97% for the three focal species, and field validation of the predicted crown objects indicated that these had user’s accuracies of 94–100%. Our results demonstrate the ability of high spatial and spectral resolution remote sensing to accurately detect non-flowering crowns of focal species within a diverse tropical forest. We attribute the success of our model to recent classification and mapping techniques adapted to species detection in diverse closed-canopy forests, which can pave the way for remote species mapping in a wider variety of ecosystems.