Understanding exciton-exciton interaction in multiply excited nanocrystals is crucial to their utilization as functional materials. Yet, for lead halide perovskite nanocryst-als, which are promising candidates for nanocrystal-based technologies, numerous contradicting values have been reported for the strength and sign of their exciton-exciton interaction. In this work, we unambiguously determine the biexciton binding energy in single cesium lead halide perovskite nanocrystals at room temperature. This is enabled by the recently introduced single-photon avalanche diode array spectrometer, capable of temporally isolating biexciton-exciton emission cascades while retaining spectral resolution. We demonstrate that CsPbBr3 nanocrystals feature an attractive exciton-exciton interaction, with a mean biexciton binding energy of 10 meV. For CsPbI3 nanocrystals, we observe a mean biexciton binding energy that is close to zero, and individual nanocrystals show either weakly attractive or weakly repulsive exciton-exciton interaction. We further show that, within ensembles of both materials, single-nanocrystal biexciton binding energies are correlated with the degree of charge-carrier confinement.