The radio-frequency spectrum corresponding to re-orientation of the proton magnetic moment in HCl35 in the presence of an external magnetic field has been obtained using the molecular beam magnetic resonance method. From the observed resonance shapes and positions, the value of the spin rotational constant of the proton in HCl35 has been determined to be |cp|=41+/-3 kc/sec. Due to the large quadrupole interaction in HCl35, the perturbation methods of data analysis used with the HF molecule were inapplicable. An approximate theory of the proton spectrum has been developed in detail to aid in the analysis of the experimental data in this case and in cases of similar intermediate coupling. Theoretical spectra were calculated on the UNIVAC computer using this approximate theory and directly compared with the experimental spectrum to estimate the value of |cp|. Theoretical spectra were also calculated on the UNIVAC using a direct solution of the Hamiltonian secular equation and were compared with the experimental curves to provide a check on the validity of the approximate theory. The comparisons indicate that the use of the approximate theory will allow the determination of |cp| to within 10%.