We report a large positive magnetoresistance ratio in insulating organic crystals theta-(ET)(2)CsZn(SCN)(4) at low temperatures at which they exhibit highly nonlinear current-voltage characteristics. Despite the nonlinearity, the magnetoresistance ratio is independent of the applied voltage. The magnetoresistance ratio depends little on the magnetic field direction and is described by a simple universal function of mu(B)B/k(B)T, where mu(B) is the Bohr magneton. The positive magnetoresistance may be caused by magnetic-field-induced parallel alignment of spins of mobile and localized electrons, and a resulting blockade of electrical conduction due to the Pauli exclusion principle.