The first purely organic BEDT-TTF spin--Peierls system, beta'-(ET)(2)SF5CF2SO3, has been confirmed using a high-frequency electron paramagnetic resonance (EPR) cavity perturbation technique. The material exhibits the characteristics of a quasi-one-dimensionai (1D) Heisenberg antiferromagnetic spin system above 30 K, but undergoes a second-order transition, at Tsp = 33 K, to a Singlet ground state, due to a progressive spin-lattice dimerization. The spin--Peierls state is evidenced by a sharp drop in the spin susceptibility below 24 K for the magnetic field (of order 2.5 T) parallel to each of the three principal axes (i.e., H \ \a, H \ \b, and H \ \c). The spin-Peierls distortion based on g value shift analysis appears to be predominately along the crystallographic b axis. The singlet-triplet gap, Delta (sigma)(0) = 114 (+/-21) K, was determined using a modified BCS theory. Also, we describe in some detail the millimeter-wave vector network analyzer (MVNA) for researchers who have interest in precision EPR measurements at magnetic fields and corresponding resonance frequencies higher than conventional X-band measurements.