Quantum mechanics postulates that the hydrogen atom has a stable ground state from which it can be promoted to excited states by capture of electromagnetic radiation, with the energy of all possible states given by E_n = −13.598/n² eV, in which n ≥ 1 is a positive integer. It has been previously proposed that the n = 1 state is not the true ground state, and that so-called hydrino states of lower energy can exist, which are characterized by fractional quantum numbers n = 1/p, in which 1 < p ≤ 137 is a limited integer. Electron transition to a hydrino state, H(1/p) is non-radiative and requires a quantized amount of energy, 2mE₁ (m is an integer), to be transferred to a catalyst. Numerous putative hydrino-forming reactions have been previously explored and the products have been characterized by a range of analytical methods. Molecular hydrino has been predicted to be paramagnetic. Here, we give an account of an electron paramagnetic resonance (EPR) study of molecular hydrino H₂(1/4) that was produced as gaseous inclusion in polymeric Ga(O)OH by a plasma reaction of atomic hydrogen with non-hydrogen bonded water as the catalyst. A sharp, complex, multi-line EPR spectrum is found, whose detailed properties prove to be consistent with predictions from hydrino theory. Molecular hydrino was also identified in gas chromatography as a compound faster than molecular hydrogen.