Knowledge of airway tree morphology has important clinical applications in diagnosis of chronic obstructive pulmonary disease. We present an automatic tree extraction method based on multiple hypothesis tracking and template matching for this purpose and evaluate its performance on chest CT images. The method is adapted from a semi-automatic method devised for vessel segmentation. Idealized tubular templates are constructed that match airway probability obtained from a trained classifier and ranked based on their relative significance. Several such regularly spaced templates form the local hypotheses used in constructing a multiple hypothesis tree, which is then traversed to reach decisions. The proposed modifications remove the need for local thresholding of hypotheses as decisions are made entirely based on statistical comparisons involving the hypothesis tree. The results show improvements in performance when compared to the original method and region growing on intensity images. We also compare the method with region growing on the probability images, where the presented method does not show substantial improvement, but we expect it to be less sensitive to local anomalies in the data. ; Comment: 12 pages. Presented at the MICCAI Pulmonary Image Analysis Workshop, Athens, Greece, 2016