Coherent anti-Stokes Raman scattering (CARS) holography captures both the amplitude and the phase of the anti-Stokes field generated from a sample and can thus perform single-shot, chemically selective three-dimensional imaging. We present compressive CARS holography, a numerical technique based on the concept of compressive sensing, to improve the quality of reconstructed images by leveraging sparsity in the source distribution and reducing the out-of-focus background noise. In particular, we use the two-step iterative shrinkage threshold (TwIST) algorithm with an l1 norm regularizer to iteratively retrieve images from an off axis CARS digital hologram. It is shown that the use of compressive CARS holography enhances the CARS holographic imaging technique by reducing noise and thereby effectively emulating a higher axial resolution using only a single shot hologram.