Linear chirps, a special case of polynomial phase exponentials, have recently been proposed for digital watermarking. In this work, we propose a known-host-state methodology for designing image watermarks that are robust to compression. We use a two-dimensional frequency-modulated chirp as a spreading function in a block-based spatial watermarking scheme. In each block, the chirp is used to embed binary phase information. Chirp parameters allow for spectral shaping of the watermark to match host content. Since host state is known to the embedder, it is possible to tune the chirp for optimum performance, particularly against compression. In contrast to existing chirp watermarking where only a single watermark is generally embedded, the proposed block chirp watermarking allows for a much higher payload. Detection is done using chirp transform subject to key exchange for security. We show that the proposed method significantly outperforms non-adaptive watermarking across all compression factors under variety of attacks.