We report the first demonstration of a regime of operation in optical parametric oscillators (OPOs), in which the formation of temporal simultons produces stable femtosecond half-harmonic pulses. Simultons are simultaneous bright-dark solitons of a signal field at frequency ω and the pump field at 2ω, which form in a quadratic nonlinear medium. The formation of simultons in an OPO is due to the interplay of nonlinear pulse acceleration with the timing mismatch between the pump repetition period and the cold-cavity round-trip time and is evidenced by sech^{2} spectra with broad instantaneous bandwidths when the resonator is detuned to a slightly longer round-trip time than the pump repetition period. We provide a theoretical description of an OPO operating in a regime dominated by these dynamics, observe the distinct features of simulton formation in an experiment, and verify our results with numerical simulations. These results represent a new regime of operation in nonlinear resonators, which can lead to efficient and scalable sources of few-cycle frequency combs at arbitrary wavelengths.