We show that a properly dc-biased Josephson junction in series with two microwave resonators of different frequencies emits photon pairs in the resonators. By measuring auto- and inter-correlations of the power leaking out of the resonators, we demonstrate two-mode amplitude squeezing below the classical limit. This non-classical microwave light emission is found to be in quantitative agreement with our theoretical predictions, up to an emission rate of 2 billion photon pairs per second.