Does overall thermal equilibrium exist between ions and electrons in a weakly collisional, magnetized, turbulent plasma? And, if not, how is thermal energy partitioned between ions and electrons? This is a fundamental question in plasma physics, the answer to which is also crucial for predicting the properties of far-distant astronomical objects such as accretion disks around black holes. In the context of disks, this question was posed nearly two decades ago and has since generated a sizeable literature. Here we provide the answer for the case in which energy is injected into the plasma via Alfvénic turbulence: Collisionless turbulent heating typically acts to disequilibrate the ion and electron temperatures. Numerical simulations using a hybrid fluid-gyrokinetic model indicate that the ion-electron heating-rate ratio is an increasing function of the thermal-to-magnetic energy ratio, [Formula: see text]: It ranges from [Formula: see text] at [Formula: see text] to at least 30 for [Formula: see text] This energy partition is approximately insensitive to the ion-to-electron temperature ratio [Formula: see text] Thus, in the absence of other equilibrating mechanisms, a collisionless plasma system heated via Alfvénic turbulence will tend toward a nonequilibrium state in which one of the species is significantly hotter than the other, i.e., hotter ions at high [Formula: see text] and hotter electrons at low [Formula: see text] Spectra of electromagnetic fields and the ion distribution function in 5D phase space exhibit an interesting new magnetically dominated regime at high [Formula: see text] and a tendency for the ion heating to be mediated by nonlinear phase mixing ("entropy cascade") when [Formula: see text] and by linear phase mixing (Landau damping) when [Formula: see text].