Chunk parsing is conceptually appealing but its performance has not been satisfactory for practical use. In this paper we show that chunk parsing can perform significantly better than previously reported by using a simple sliding-window method and maximum entropy classifiers for phrase recognition in each level of chunking. Experimental results with the Penn Treebank corpus show that our chunk parser can give high-precision parsing outputs with very high speed (14 msec/sentence). We also present a parsing method for searching the best parse by considering the probabilities output by the maximum entropy classifiers, and show that the search method can further improve the parsing accuracy.