The sensitivity limitations for magnetic resonance imaging of organic molecules have recently been addressed by hyperpolarization methods, which prepare excess nuclear spin polarization. This approach can increase sensitivity by orders of magnitude, but the enhanced signal relaxes away in tens of seconds, even in favorable cases. Here we show theoretically that singlet states between strongly coupled spins in molecules can be used to store and retrieve population in very-long-lived disconnected eigenstates, as long as the coupling between the spins substantially exceeds both the couplings to other spins and the resonance frequency difference between them. Experimentally, 2,3-carbon-13-labeled diacetyl has a disconnected eigenstate that can store population for minutes and is read out by hydration to make the two spins inequivalent.