Recent Chandra X-ray observations of globular clusters have identified numerous accreting neutron stars (NSs) in quiescence, with spectra generally well-described by hydrogen atmosphere models. Spectral analysis of these systems at known distances offers the promise of constraints upon the mass and radius of the NS. The brightest of these systems, X7 in 47 Tuc, requires a mass greater than 2 solar masses to fit a radius between 9 and 16 km. This conclusion may be avoided if continued accretion is altering the opacity of the atmosphere.