Chart constraints, which specify at which string positions a constituent may begin or end, have been shown to speed up chart parsers for PCFGs. We generalize chart constraints to more expressive grammar formalisms and describe a neural tagger which predicts chart constraints at very high precision. Our constraints accelerate both PCFG and TAG parsing, and combine effectively with other pruning techniques (coarse-to-fine and supertagging) for an overall speedup of two orders of magnitude, while improving accuracy.