  We investigate quantum properties of light in optical parametric oscillators
(OPOs) based on four-wave mixing gain in media with third-order
non-linearities. In spite of other competing $\chi^{(3)}$ effects, such as
phase modulation, bipartite and tripartite entanglement are predicted above
threshold. These findings are relevant for recent implementations of
CMOS-compatible on-chip OPOs.
