Polar codes have been shown to provide an effective mechanism for achieving physical-layer security over various wiretap channels. A majority of these schemes require channel state information (CSI) at the encoder for both intended receivers and eavesdroppers. In this paper, we consider a polar coding scheme for secrecy over a Gaussian wiretap channel when no CSI is available. We show that the availability of a shared keystream between friendly parties allows polar codes to be used for both secure and reliable communications, even when the eavesdropper knows a large fraction of the keystream. The scheme relies on a predetermined strategy for partitioning the bits to be encoded into a set of frozen bits and a set of information bits. The frozen bits are filled with bits from the keystream, and we evaluate the security gap when the cyclic redundancy check-aided successive cancellation list decoder is used at both receivers in the wiretap channel model.