We present a classifier-based parser that produces constituent trees in linear time. The parser uses a basic bottom-up shift-reduce algorithm, but employs a classifier to determine parser actions instead of a grammar. This can be seen as an extension of the deterministic dependency parser of Nivre and Scholz (2004) to full constituent parsing. We show that, with an appropriate feature set used in classification, a very simple one-path greedy parser can perform at the same level of accuracy as more complex parsers. We evaluate our parser on section 23 of the WSJ section of the Penn Treebank, and obtain precision and recall of 87.54% and 87.61%, respectively.