We present a constituency parsing algorithm that, like a supertagger, works by assigning labels to each word in a sentence. In order to maximally leverage current neural architectures, the model scores each word's tags in parallel, with minimal task-specific structure. After scoring, a left-to-right reconciliation phase extracts a tree in (empirically) linear time. Our parser achieves 95.4 F1 on the WSJ test set while also achieving substantial speedups compared to current state-of-the-art parsers with comparable accuracies.