This paper aims at filling the gap between the accuracy of Italian and English constituency parsing: firstly, we adapt the Bllip parser, i.e., the most accurate constituency parser for English, also known as Charniak parser, for Italian and trained it on the Turin University Treebank (TUT). Secondly, we design a parse reranker based on Support Vector Machines using tree kernels, where the latter can effectively generalize syntactic patterns, requiring little training data for training the model. We show that our approach outperforms the state of the art achieved by the Berkeley parser, improving it from 84.54 to 86.81 in labeled F1.