This 3-part study will evaluate the efficacy and safety of an oral kallikrein inhibitor, BCX7353, in the treatment angioedema attacks in subjects with Type I or II hereditary angioedema (HAE). In each study part, subjects will treat 3 attacks with BCX7353 (2 attacks) or placebo (1 attack), in a randomly allocated order. In Part 1, the dose of 750mg will be assessed relative to placebo in up to 36 patients. If this is shown to be effective, then a further 12 patients will be enrolled at a 500mg dose (Part 1), followed by a further 12 (if efficacy still shown) at a dose of 250mg (Part 3) to determine the minimum effective dose of BCX7353 compared to placebo for treating HAE attacks. Efficacy will be determined by subject diary entries completed at pre-defined times post-dose.