We present a new, efficient frame-semantic parser that labels semantic arguments to FrameNet predicates. Built using an extension to the segmental RNN that emphasizes recall, our basic system achieves competitive performance without any calls to a syntactic parser. We then introduce a method that uses phrase-syntactic annotations from the Penn Treebank during training only, through a multitask objective; no parsing is required at training or test time. This "syntactic scaffold" offers a cheaper alternative to traditional syntactic pipelining, and achieves state-of-the-art performance.