We present a strictly lexical parsing model where all the parameters are based on the words. This model does not rely on part-of-speech tags or grammatical categories. It maximizes the conditional probability of the parse tree given the sentence. This is in contrast with most previous models that compute the joint probability of the parse tree and the sentence. Although the maximization of joint and conditional probabilities are theoretically equivalent, the conditional model allows us to use distributional word similarity to generalize the observed frequency counts in the training corpus. Our experiments with the Chinese Treebank show that the accuracy of the conditional model is 13.6% higher than the joint model and that the strictly lexicalized conditional model outperforms the corresponding unlexicalized model based on part-of-speech tags.