This study investigated the relationship of speech intelligibility and the narrative comprehension among bilingual kindergarten children and how well the speech intelligibility of second language (L2) predicted the L2 narrative comprehension using a machine learning approach. Fifty Chinese-English bilingual children aged 5-6 years old participated in this study by taking a narrative comprehension test. Their L2 narrative comprehension was assessed using the MAIN test. The speech intelligibility was assessed in terms of twenty-four features that encode confidence levels with respect to phoneme and word classifiers trained on native speaker speech data. Our hypothesis posits that it is possible to predict L2 narrative comprehension based on speech intelligibility features. By using seven out of the twenty-four considered features we were able to make predictions of the MAIN test scores with an RMSE of 2.13 and a Pearson correlation coefficient of 0.468 based on a data set of 50 bilingual kindergarten children. We conclude the paper by providing pedagogical implications for second language teaching as well as suggestions for future work.