Setting out from the point of view that automatic speech recognition (ASR) ought to benefit from data in languages other than the target language, we propose a novel Kullback-Leibler (KL) divergence based method that is able to exploit multilingual information in the form of universal phoneme posterior probabilities conditioned on the acoustics. We formulate a means to train a recognizer on several different languages, and subsequently recognize speech in a target language for which only a small amount of data is available. Taking the Greek SpeechDat(II) data as an example, we show that the proposed formulation is sound, and show that it is able to outperform a current state-of-the-art HMM/GMM system. We also use a hybrid Tandem-like system to further understand the source of the benefit.