  Atomic comagnetometers are used in searches for anomalous spin-dependent
interactions. Magnetic field gradients are one of the major sources of
systematic errors in such experiments. Here we describe a comagnetometer based
on the nuclear spins within an ensemble of identical molecules. The dependence
of the measured spin-precession frequency ratio on the first-order magnetic
field gradient is suppressed by over an order of magnitude compared to a
comagnetometer based on overlapping ensembles of different molecules. Our
single-species comagnetometer is shown to be capable of measuring the
hypothetical spin-dependent gravitational energy of nuclei at the $10^{-17}$ eV
level, comparable to the most stringent existing constraints. Combined with
techniques for enhancing the signal such as parahydrogen-induced polarization,
this method of comagnetometry offers the potential to improve constraints on
spin-gravity coupling of nucleons by several orders of magnitude.
