We describe a new method for phoneme sequence recognition given a speech utterance. In contrast to HMM-based approaches, our method uses a kernel-based discriminative training procedure in which the learning process is tailored to the goal of minimizing the Levenshtein distance between the predicted phoneme sequence and the correct sequence. The phoneme sequence predictor is devised by mapping the speech utterance along with a proposed phoneme sequence to a vector-space endowed with an inner-product that is realized by a Mercer kernel. Building on large margin techniques for predicting whole sequences, we are able to devise a learning algorithm which distills to separating the correct phoneme sequence from all other sequences. We describe an iterative algorithm for learning the phoneme sequence recognizer and further describe an efficient implementation of it. We present initial encouraging experimental results with the TIMIT and compare the proposed method to an HMM-based approach.