We have obtained I-, J-, H- and K-band light curves of the recurrent nova TCrB. We find that we can fit the J-band light curve only with a Roche lobe filling secondary star and a dark spot of radius 11 deg-26 deg (90 per cent confidence) centred at the inner Lagrangian point. We obtain limits to the binary inclination of 38 deg-46 deg (90 per cent confidence) which, when combined with the value for the mass function, allow us to determine the mass of the compact object to be 1.3-2.5 Msolar (90 per cent confidence). This mass range is consistent with the Chandrasekhar limiting white dwarf mass, and so we provide evidence needed to support the outbursts in recurrent novae in terms of a thermonuclear runaway process on the surface of a massive ~1.4-Msolar white dwarf.