We use an effective model to calculate properties of the supercurrent carried by chiral edge states of a quantum Hall weak link. This "chiral" supercurrent is qualitatively distinct from the usual Josephson supercurrent in that it cannot be mediated by a single edge alone, i.e., both right- and left-going edges are needed. Moreover, the chiral supercurrent was previously shown to obey an unusual current-phase relation with period 2 phi(0) = h/e, which is twice the period of conventional Josephson junctions. We show that the "chiral" nature of this supercurrent is sharply defined, and is robust to interactions to infinite order in perturbation theory. We compare our results with recent experimental findings [Amet et al., Science 352 966 (2016)] and find that quantitative agreement in the magnitude of the supercurrent can be attained by making reasonable but critical assumptions about the superconductor quantum Hall interface.