Prior work on criminal incident prediction has relied primarily on the historical crime record and various geospatial and demographic information sources. Although promising, these models do not take into account the rich and rapidly expanding social media context that surrounds incidents of interest. This paper presents a preliminary investigation of Twitter-based criminal incident prediction. Our approach is based on the automatic semantic analysis and understanding of natural language Twitter posts, combined with dimensionality reduction via latent Dirichlet allocation and prediction via linear modeling. We tested our model on the task of predicting future hit-and-run crimes. Evaluation results indicate that the model comfortably outperforms a baseline model that predicts hit-and-run incidents uniformly across all days.