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Encrypted voice-over-IP (VoIP) communication often uses variable bit rate (VBR) codecs to achieve good audio quality while minimizing bandwidth costs. Prior work has shown that encrypted VBR-based VoIP streams are vulnerable to re-identification attacks in which an attacker can infer attributes (e.g., the language being spoken, the identities of the speakers, and key phrases) about the underlying audio by analyzing the distribution of packet sizes. Existing defenses require the participation of both the sender and receiver to secure their VoIP communications. This paper presents Whisper, the first unilateral defense against re-identification attacks on encrypted VoIP streams. Whisper works by modifying the audio signal before it is encoded by the VBR codec, adding inaudible audio that either falls outside the fixed range of human hearing or is within the human audible range but is nearly imperceptible due to its low amplitude. By carefully inserting such noise, Whisper modifies the audio stream's distribution of packet sizes, significantly decreasing the accuracy of re-identification attacks. Its use is imperceptible by the (human) receiver. Whisper can be instrumented as an audio driver and requires no changes to existing (potentially closed-source) VoIP software. Since it is a unilateral defense, it can be applied at will by a user to enhance the privacy of its voice communications. We demonstrate that Whisper significantly reduces the accuracy of re-identification attacks and incurs only a small degradation in audio quality.