The heterogeneous cellular network (HCN) is a promising approach to the deployment of 5G cellular networks. This paper comprehensively studies physical layer security in a multitier HCN where base stations (BSs), authorized users, and eavesdroppers are all randomly located. We first propose an access threshold-based secrecy mobile association policy that associates each user with the BS providing the maximum truncated average received signal power beyond a threshold. Under the proposed policy, we investigate the connection probability and secrecy probability of a randomly located user and provide tractable expressions for the two metrics. Asymptotic analysis reveals that setting a larger access threshold increases the connection probability while decreases the secrecy probability. We further evaluate the network-wide secrecy throughput and the minimum secrecy throughput per user with both connection and secrecy probability constraints. We show that introducing a properly chosen access threshold significantly enhances the secrecy throughput performance of a HCN.