We present the first measurement of two-mode squeezing between the twin beams produced by a doubly resonant optical parameter oscillator (OPO) in an above threshold operation based on parametric amplification by nondegenerate four wave mixing with rubidium (^{85}Rb). We demonstrate a maximum intensity difference squeezing of -2.7  dB (-3.5  dB corrected for losses) with a pump power of 285 mW and an output power of 12 mW for each beam, operating close to the D1 line of Rb atoms. The use of open cavities combined with the high gain media can provide a strong level of noise compression and the access to new operation regimes that could not be explored by crystal based OPOs. The spectral bandwidth of the squeezed light is broadened by the cavity dynamics, and the squeezing level is robust for strong pump powers. Stable operation was obtained up to 4 times above the threshold. Moreover, operation of the OPO close to the atomic resonances of alkali atoms allows a natural integration into quantum networks, including structures such as quantum memories.