We introduce a new benchmark dataset, namely VinDr-RibCXR, for automatic segmentation and labeling of individual ribs from chest X-ray (CXR) scans. The VinDr-RibCXR contains 245 CXRs with corresponding ground truth annotations provided by human experts. A set of state-of-the-art segmentation models are trained on 196 images from the VinDr-RibCXR to segment and label 20 individual ribs. Our best performing model obtains a Dice score of 0.834 (95% CI, 0.810--0.853) on an independent test set of 49 images. Our study, therefore, serves as a proof of concept and baseline performance for future research.