We demonstrate a degenerate parametric oscillator in a silicon nitride microresonator. We use two frequency-detuned pump waves to perform parametric four-wave mixing and operate in the normal group-velocity dispersion regime to produce signal and idler fields that are frequency degenerate. Our theoretical modeling shows that this regime enables generation of bimodal phase states, analogous to the χ(2)-based degenerate OPO. Our system offers potential for realization of CMOS-chip-based coherent optical computing and an all-optical quantum random number generator.