Tree species identification is critical to support their conservation, sustainable management and, particularly, the fight against illegal logging. Therefore, it is very important to develop fast and accurate identification systems even for non-experts. In this research we have achieved three main results. First, we developed -- from scratch and using new sample collecting and processing protocols -- an dataset called CRTreeCuts that comprises macroscopic cross-section images of 147 native tree species from Costa Rica. Secondly, we implemented a CNN for automated tree species identification based on macroscopic images of cross-sections of wood. For this CNN we apply the fine-tuning technique with VGG16 as a base model, pre-trained with the ImageNet data set. This model is trained and tested with a subset of 75 species from CRTreeCuts. The top-1 and top-3 accuracies achieved in the testing phase are 70.5% and 80.3%, respectively. The Same-Specimen-Picture Bias (SSPB), which is known to erroneously increase accuracy, is absent in all experiments. Finally, the third result is Cocobolo, an Android mobile application that uses the developed CNN as back-end to identify Costa Rican tree species from images of a cross-sections of wood.