A new technique is presented for securing a space-time block code in the presence of an eavesdropper without channel state information (CSI) at the transmitter. Assuming channel reciprocity between the transmitter and the intended receiver, we use the receive signal strength indicator, which is much easier to estimate reliably than CSI, to randomly rotate the information symbols at each transmit antenna without increasing the transmit signal's peak-to-average ratio. It is shown that the proposed scheme guarantees full diversity to an intended recipient while reducing the diversity order of an eavesdropper to zero even in the presence of perfect channel state information.