Identifying X-ray binary (XRB) candidates in nearby galaxies requires distinguishing them from possible contaminants including foreground stars and background active galactic nuclei. This work investigates the use of supervised machine learning algorithms to identify high-probability X-ray binary candidates. Using a catalogue of 943 Chandra X-ray sources in the Andromeda galaxy, we trained and tested several classification algorithms using the X-ray properties of 163 sources with previously known types. Amongst the algorithms tested, we find that random forest classifiers give the best performance and work better in a binary classification (XRB/non-XRB) context compared to the use of multiple classes. Evaluating our method by comparing with classifications from visible-light and hard X-ray observations as part of the Panchromatic Hubble Andromeda Treasury, we find compatibility at the 90% level, although we caution that the number of source in common is rather small. The estimated probability that an object is an X-ray binary agrees well between the random forest binary and multiclass approaches and we find that the classifications with the highest confidence are in the X-ray binary class. The most discriminating X-ray bands for classification are the 1.7-2.8, 0.5-1.0, 2.0-4.0, and 2.0-7.0 keV photon flux ratios. Of the 780 unclassified sources in the Andromeda catalogue, we identify 16 new high-probability X-ray binary candidates and tabulate their properties for follow-up.