Abstract An idealized aquaplanet moist global atmospheric model with realistic radiative transfer but no clouds and no convective parameterization is found to possess multiple climate equilibria. When forced symmetrically about the equator, in some cases the Inter Tropical Convergence Zone (ITCZ) migrates to an off‐equatorial equilibrium position. Mechanism denial experiments prescribing relative humidity imply that radiation‐circulation coupling is essential to this instability. The cross‐equatorial asymmetry occurs only when the underlying slab ocean is sufficiently deep and the atmosphere's spectral dynamical core is sufficiently coarse (∼T170 or less with our control parameters). At higher resolutions, initializing with an asymmetric state indicates metastability with very slow (thousands of days) return to hemispheric symmetry. There is some sensitivity to the model timestep, which affects the time required to transition to the asymmetric state, with little effect on the equilibrium climate. The instability is enhanced when the planetary boundary layer scheme favors deeper layers or by a prescribed meridional heat transport away from the equator within the slab. The instability is not present when the model is run with a convective parameterization scheme commonly utilized in idealized moist models. We argue that the instability occurs when the asymmetric heating associated with a spontaneous ITCZ shift drives a circulation that rises poleward of the perturbed ITCZ. These results serve as a warning of the potential for instability and non‐uniqueness of climate that may complicate studies with idealized models of the tropical response to perturbations in forcing.