Deep learning methods have enabled taskoriented semantic parsing of increasingly complex utterances. However, a single model is still typically trained and deployed for each task separately, requiring labeled training data for each, which makes it challenging to support new tasks, even within a single business vertical (e.g., food-ordering or travel booking). In this paper we describe Cross-TOP (Cross-Schema Task-Oriented Parsing), a zero-shot method for complex semantic parsing in a given vertical. By leveraging the fact that user requests from the same vertical share lexical and semantic similarities, a single cross-schema parser is trained to service an arbitrary number of tasks, seen or unseen, within a vertical. We show that Cross-TOP can achieve high accuracy on a previously unseen task without requiring any additional training data, thereby providing a scalable way to bootstrap semantic parsers for new tasks. As part of this work we release the FoodOrdering dataset, a task-oriented parsing dataset in the food-ordering vertical, with utterances and annotations derived from five schemas, each from a different restaurant menu.