We present an implementation of a chart-based head-corner parsing algorithm for lexicalized Tree Adjoining Grammars. We report on some practical experiments where we parse 2250 sentences from the Wall Street Journal using this parser. In these experiments the parser is run without any statistical pruning; it produces all valid parses for each sentence in the form of a shared derivation forest. The parser uses a large Treebank Grammar with 6789 tree templates with about 120# 000 lexicalized trees. The results suggest that the observed complexity of parsing for LTAG is dominated by factors other than sentence length. 1. Motivation The particular experiments that we report on in this paper were chosen to discover certain facts about LTAG parsing in a practical setting. Specifically, we wanted to discover the importance of the worst-case results for LTAG parsing in practice. Let us take Schabes' Earleystyle TAG parsing algorithm (Schabes, 1994) which is the usual candidate for a practica...