In this paper, the secure transmission of information over an ergodic fading channel is investigated in the presence of statistical quality of service (QoS) constraints. We employ effective capacity, which provides the maximum constant arrival rate that a given process can support while satisfying statistical delay constraints, to measure the secure throughput of the system, i.e., effective secure throughput. We assume that the channel side information (CSI) of the main channel is available at the transmitter side. Depending on the availability of the CSI of the eavesdropper channel, we obtain the corresponding optimal power control policies that maximize the effective secure throughput. In particular, when the CSI of the eavesdropper channel is available at the transmitter, the transmitter can no longer wait for transmission when the main channel is much better than the eavesdropper channel due to the introduction of QoS constraints. Moreover, the CSI of the eavesdropper channel becomes useless as QoS constraints become stringent.