We report spatially resolved spectroscopy of both components of the low-mass pre-main-sequence binary GV Tau. High resolution spectroscopy in the K- and L-bands is used to characterize the stellar properties of the binary and to explore the nature of the circumstellar environment. We find that the southern component, GV Tau S, is a radial velocity variable, possibly as a result of an unseen low-mass companion. The strong warm gaseous HCN absorption reported previously toward GV Tau S (Gibb et al. 2007) was not present during the epoch of our observations. Instead, we detect warm (~500 K) molecular absorption with similar properties toward the northern infrared companion, GV Tau N. At the epoch of our observations, the absorbing gas toward GV Tau N was approximately at the radial velocity of the GV Tau molecular envelope, but it was redshifted with respect to the star by ~13 km/s. One interpretation of our results is that GV Tau N is also a binary and that most of the warm molecular absorption arises in a circumbinary disk viewed close to edge-on.