There is a rapidly increasing amount of research on the use of brain activity patterns as a basis for biometric user verification. The vast majority of this research is based on Electroencephalogram (EEG), a technology which measures the electrical activity along the scalp. In this paper, we evaluate Functional Near-Infrared Spectroscopy (fNIRS) as an alternative approach to brain activity-based user authentication. fNIRS is centered around the measurement of light absorbed by blood and, compared to EEG, has a higher signal-to-noise ratio, is more suited for use during normal working conditions, and has a much higher spatial resolution which enables targeted measurements of specific brain regions. Based on a dataset of 50 users that was analysed using an SVM and a Naïve Bayes classifier, we show fNIRS to respectively give EERs of 0.036 and 0.046 when using our best channel configuration. Further, we present some results on the areas of the brain which demonstrated highest discriminative power. Our findings indicate that fNIRS has significant promise as a biometric authentication modality.